By plotting y = (x-1/50)^2 - floor(x^2) it can be seen that solutions start at x = 0, and continue until around x = 25. So we solve the equation substituting integers from 0 through 627 to see if there are solutions and if the solutions squares have floors that match the substituted number:
floor of
square
attempt
found x full x^2
0 0 1/50 0.0004000000000**
1 1 51/50 1.0404000000000**
2 2 2^(1/2) + 1/50 2.0569685424949
3 3 3^(1/2) + 1/50 3.0696820323028
4 4 101/50 4.0804000000000**
5 5 5^(1/2) + 1/50 5.0898427191000
6 6 6^(1/2) + 1/50 6.0983795897113
7 7 7^(1/2) + 1/50 7.1062300524426
8 8 8^(1/2) + 1/50 8.1135370849898
9 9 151/50 9.1204000000000**
10 10 10^(1/2) + 1/50 10.1268911064067
11 11 11^(1/2) + 1/50 11.1330649916142
12 12 12^(1/2) + 1/50 12.1389640646055
13 13 13^(1/2) + 1/50 13.1446220510186
14 14 14^(1/2) + 1/50 14.1500662954710
15 15 15^(1/2) + 1/50 15.1553193338483
16 16 201/50 16.1604000000000**
17 17 17^(1/2) + 1/50 17.1653242250247
18 18 18^(1/2) + 1/50 18.1701056274848
19 19 19^(1/2) + 1/50 19.1747559577416
20 20 20^(1/2) + 1/50 20.1792854382000
21 21 21^(1/2) + 1/50 21.1837030277982
22 22 22^(1/2) + 1/50 22.1880166303929
23 23 23^(1/2) + 1/50 23.1922332609325
24 24 24^(1/2) + 1/50 24.1963591794226
25 25 251/50 25.2004000000000**
26 26 26^(1/2) + 1/50 26.2043607805437
27 27 27^(1/2) + 1/50 27.2082460969083
28 28 28^(1/2) + 1/50 28.2120601048852
29 29 29^(1/2) + 1/50 29.2158065922854
30 30 30^(1/2) + 1/50 30.2194890230021
31 31 31^(1/2) + 1/50 31.2231105745132
32 32 4*2^(1/2) + 1/50 32.2266741699797
33 33 33^(1/2) + 1/50 33.2301825058615
34 34 34^(1/2) + 1/50 34.2336380757938
35 35 35^(1/2) + 1/50 35.2370431913240
36 36 301/50 36.2404000000000**
37 37 37^(1/2) + 1/50 37.2437105012119
38 38 38^(1/2) + 1/50 38.2469765601187
39 39 39^(1/2) + 1/50 39.2501999199359
40 40 40^(1/2) + 1/50 40.2533822128135
41 41 41^(1/2) + 1/50 41.2565249694973
42 42 42^(1/2) + 1/50 42.2596296279363
43 43 43^(1/2) + 1/50 43.2626975409721
44 44 44^(1/2) + 1/50 44.2657299832284
45 45 3*5^(1/2) + 1/50 45.2687281573000
46 46 46^(1/2) + 1/50 46.2716931993250
47 47 47^(1/2) + 1/50 47.2746261840160
48 48 4*3^(1/2) + 1/50 48.2775281292110
49 49 351/50 49.2804000000000**
50 50 5*2^(1/2) + 1/50 50.2832427124746
51 51 51^(1/2) + 1/50 51.2860571371417
52 52 52^(1/2) + 1/50 52.2888441020371
53 53 53^(1/2) + 1/50 53.2916043955712
54 54 3*6^(1/2) + 1/50 54.2943387691340
55 55 55^(1/2) + 1/50 55.2970479394838
56 56 56^(1/2) + 1/50 56.2997325909419
57 57 57^(1/2) + 1/50 57.3023933774108
58 58 58^(1/2) + 1/50 58.3050309242346
59 59 59^(1/2) + 1/50 59.3076458299147
60 60 60^(1/2) + 1/50 60.3102386676966
61 61 61^(1/2) + 1/50 61.3128099870363
62 62 62^(1/2) + 1/50 62.3153603149605
63 63 3*7^(1/2) + 1/50 63.3178901573278
64 64 401/50 64.3204000000000**
65 65 65^(1/2) + 1/50 65.3228903099319
66 66 66^(1/2) + 1/50 66.3253615361854
67 67 67^(1/2) + 1/50 67.3278141108749
68 68 68^(1/2) + 1/50 68.3302484500494
69 69 69^(1/2) + 1/50 69.3326649545167
70 70 70^(1/2) + 1/50 70.3350640106136
71 71 71^(1/2) + 1/50 71.3374459909271
72 72 6*2^(1/2) + 1/50 72.3398112549695
73 73 73^(1/2) + 1/50 73.3421601498127
74 74 74^(1/2) + 1/50 74.3444930106817
75 75 5*3^(1/2) + 1/50 75.3468101615138
76 76 76^(1/2) + 1/50 76.3491119154833
77 77 77^(1/2) + 1/50 77.3513985754957
78 78 78^(1/2) + 1/50 78.3536704346531
79 79 79^(1/2) + 1/50 79.3559277766926
80 80 4*5^(1/2) + 1/50 80.3581708764000
81 81 451/50 81.3604000000000**
82 82 82^(1/2) + 1/50 82.3626154055255
83 83 83^(1/2) + 1/50 83.3648173431658
84 84 84^(1/2) + 1/50 84.3670060555964
85 85 85^(1/2) + 1/50 85.3691817782917
86 86 86^(1/2) + 1/50 86.3713447398198
87 87 87^(1/2) + 1/50 87.3734951621236
88 88 88^(1/2) + 1/50 88.3756332607859
89 89 89^(1/2) + 1/50 89.3777592452822
90 90 3*10^(1/2) + 1/50 90.3798733192202
91 91 91^(1/2) + 1/50 91.3819756805668
92 92 92^(1/2) + 1/50 92.3840665218650
93 93 93^(1/2) + 1/50 93.3861460304397
94 94 94^(1/2) + 1/50 94.3882143885933
95 95 95^(1/2) + 1/50 95.3902717737923
96 96 4*6^(1/2) + 1/50 96.3923183588453
97 97 97^(1/2) + 1/50 97.3943543120718
98 98 7*2^(1/2) + 1/50 98.3963797974645
99 99 3*11^(1/2) + 1/50 99.3983949748426
100 100 501/50 100.4004000000000**
101 101 101^(1/2) + 1/50 101.4023950248448
102 102 102^(1/2) + 1/50 102.4043801975345
103 103 103^(1/2) + 1/50 103.4063556626037
104 104 104^(1/2) + 1/50 104.4083215610874
105 105 105^(1/2) + 1/50 105.4102780306384
106 106 106^(1/2) + 1/50 106.4122252056395
107 107 107^(1/2) + 1/50 107.4141632173116
108 108 6*3^(1/2) + 1/50 108.4160921938165
109 109 109^(1/2) + 1/50 109.4180122603564
110 110 110^(1/2) + 1/50 110.4199235392681
111 111 111^(1/2) + 1/50 111.4218261501141
112 112 4*7^(1/2) + 1/50 112.4237202097703
113 113 113^(1/2) + 1/50 113.4256058325094
114 114 114^(1/2) + 1/50 114.4274831300812
115 115 115^(1/2) + 1/50 115.4293522117905
116 116 116^(1/2) + 1/50 116.4312131845707
117 117 3*13^(1/2) + 1/50 117.4330661530556
118 118 118^(1/2) + 1/50 118.4349112196480
119 119 119^(1/2) + 1/50 119.4367484845854
120 120 120^(1/2) + 1/50 120.4385780460041
121 121 551/50 121.4404000000000**
122 122 122^(1/2) + 1/50 122.4422144406875
123 123 123^(1/2) + 1/50 123.4440214602564
124 124 124^(1/2) + 1/50 124.4458211490264
125 125 5*5^(1/2) + 1/50 125.4476135955000
126 126 3*14^(1/2) + 1/50 126.4493988864129
127 127 127^(1/2) + 1/50 127.4511771067834
128 128 8*2^(1/2) + 1/50 128.4529483399594
129 129 129^(1/2) + 1/50 129.4547126676640
130 130 130^(1/2) + 1/50 130.4564701700396
131 131 131^(1/2) + 1/50 131.4582209256904
132 132 132^(1/2) + 1/50 132.4599650117230
133 133 133^(1/2) + 1/50 133.4617025037868
134 134 134^(1/2) + 1/50 134.4634334761116
135 135 3*15^(1/2) + 1/50 135.4651580015449
136 136 136^(1/2) + 1/50 136.4668761515876
137 137 137^(1/2) + 1/50 137.4685879964288
138 138 138^(1/2) + 1/50 138.4702936049788
139 139 139^(1/2) + 1/50 139.4719930449020
140 140 140^(1/2) + 1/50 140.4736863826480
141 141 141^(1/2) + 1/50 141.4753736834815
142 142 142^(1/2) + 1/50 142.4770550115125
143 143 143^(1/2) + 1/50 143.4787304297241
144 144 601/50 144.4804000000000**
145 145 145^(1/2) + 1/50 145.4820637831517
146 146 146^(1/2) + 1/50 146.4837218389438
147 147 7*3^(1/2) + 1/50 147.4853742261193
148 148 148^(1/2) + 1/50 148.4870210024238
149 149 149^(1/2) + 1/50 149.4886622246293
150 150 5*6^(1/2) + 1/50 150.4902979485566
151 151 151^(1/2) + 1/50 151.4919282290978
152 152 152^(1/2) + 1/50 152.4935531202375
153 153 3*17^(1/2) + 1/50 153.4951726750741
154 154 154^(1/2) + 1/50 154.4967869458396
155 155 155^(1/2) + 1/50 155.4983959839196
156 156 156^(1/2) + 1/50 156.4999998398719
157 157 157^(1/2) + 1/50 157.5015985634456
158 158 158^(1/2) + 1/50 158.5031922035991
159 159 159^(1/2) + 1/50 159.5047808085167
160 160 4*10^(1/2) + 1/50 160.5063644256269
161 161 161^(1/2) + 1/50 161.5079431016180
162 162 9*2^(1/2) + 1/50 162.5095168824543
163 163 163^(1/2) + 1/50 163.5110858133921
164 164 164^(1/2) + 1/50 164.5126499389946
165 165 165^(1/2) + 1/50 165.5142093031466
166 166 166^(1/2) + 1/50 166.5157639490690
167 167 167^(1/2) + 1/50 167.5173139193328
168 168 168^(1/2) + 1/50 168.5188592558726
169 169 651/50 169.5204000000000**
170 170 170^(1/2) + 1/50 170.5219361924162
171 171 3*19^(1/2) + 1/50 171.5234678732249
172 172 172^(1/2) + 1/50 172.5249950819441
173 173 173^(1/2) + 1/50 173.5265178575186
174 174 174^(1/2) + 1/50 174.5280362383309
175 175 5*7^(1/2) + 1/50 175.5295502622129
176 176 4*11^(1/2) + 1/50 176.5310599664568
177 177 177^(1/2) + 1/50 177.5325653878260
178 178 178^(1/2) + 1/50 178.5340665625650
179 179 179^(1/2) + 1/50 179.5355635264104
180 180 6*5^(1/2) + 1/50 180.5370563146000
181 181 181^(1/2) + 1/50 181.5385449618829
182 182 182^(1/2) + 1/50 182.5400295025293
183 183 183^(1/2) + 1/50 183.5415099703387
184 184 184^(1/2) + 1/50 184.5429863986500
185 185 185^(1/2) + 1/50 185.5444588203494
186 186 186^(1/2) + 1/50 186.5459272678794
187 187 187^(1/2) + 1/50 187.5473917732471
188 188 188^(1/2) + 1/50 188.5488523680321
189 189 3*21^(1/2) + 1/50 189.5503090833947
190 190 190^(1/2) + 1/50 190.5517619500836
191 191 191^(1/2) + 1/50 191.5532109984434
192 192 8*3^(1/2) + 1/50 192.5546562584220
193 193 193^(1/2) + 1/50 193.5560977595780
194 194 194^(1/2) + 1/50 194.5575355310874
195 195 195^(1/2) + 1/50 195.5589696017507
196 196 701/50 196.5604000000000**
197 197 197^(1/2) + 1/50 197.5618267539047
198 198 3*22^(1/2) + 1/50 198.5632498911788
199 199 199^(1/2) + 1/50 199.5646694391866
200 200 10*2^(1/2) + 1/50 200.5660854249493
201 201 201^(1/2) + 1/50 201.5674978751503
202 202 202^(1/2) + 1/50 202.5689068161421
203 203 203^(1/2) + 1/50 203.5703122739510
204 204 204^(1/2) + 1/50 204.5717142742834
205 205 205^(1/2) + 1/50 205.5731128425311
206 206 206^(1/2) + 1/50 206.5745080037763
207 207 3*23^(1/2) + 1/50 207.5758997827975
208 208 4*13^(1/2) + 1/50 208.5772882040742
209 209 209^(1/2) + 1/50 209.5786732917920
210 210 210^(1/2) + 1/50 210.5800550698476
211 211 211^(1/2) + 1/50 211.5814335618533
212 212 212^(1/2) + 1/50 212.5828087911424
213 213 213^(1/2) + 1/50 213.5841807807730
214 214 214^(1/2) + 1/50 214.5855495535331
215 215 215^(1/2) + 1/50 215.5869151319446
216 216 6*6^(1/2) + 1/50 216.5882775382679
217 217 217^(1/2) + 1/50 217.5896367945062
218 218 218^(1/2) + 1/50 218.5909929224093
219 219 219^(1/2) + 1/50 219.5923459434779
220 220 220^(1/2) + 1/50 220.5936958789677
221 221 221^(1/2) + 1/50 221.5950427498927
222 222 222^(1/2) + 1/50 222.5963865770300
223 223 223^(1/2) + 1/50 223.5977273809227
224 224 4*14^(1/2) + 1/50 224.5990651818838
225 225 751/50 225.6004000000000**
226 226 226^(1/2) + 1/50 226.6017318551349
227 227 227^(1/2) + 1/50 227.6030607669328
228 228 228^(1/2) + 1/50 228.6043867548217
229 229 229^(1/2) + 1/50 229.6057098380169
230 230 230^(1/2) + 1/50 230.6070300355241
231 231 231^(1/2) + 1/50 231.6083473661428
232 232 232^(1/2) + 1/50 232.6096618484691
233 233 233^(1/2) + 1/50 233.6109735008989
234 234 3*26^(1/2) + 1/50 234.6122823416311
235 235 235^(1/2) + 1/50 235.6135883886702
236 236 236^(1/2) + 1/50 236.6148916598295
237 237 237^(1/2) + 1/50 237.6161921727336
238 238 238^(1/2) + 1/50 238.6174899448216
239 239 239^(1/2) + 1/50 239.6187849933496
240 240 4*15^(1/2) + 1/50 240.6200773353932
241 241 241^(1/2) + 1/50 241.6213669878504
242 242 11*2^(1/2) + 1/50 242.6226539674442
243 243 9*3^(1/2) + 1/50 243.6239382907247
244 244 244^(1/2) + 1/50 244.6252199740725
245 245 7*5^(1/2) + 1/50 245.6264990337000
246 246 246^(1/2) + 1/50 246.6277754856543
247 247 247^(1/2) + 1/50 247.6290493458201
248 248 248^(1/2) + 1/50 248.6303206299209
249 249 249^(1/2) + 1/50 249.6315893535223
250 250 5*10^(1/2) + 1/50 250.6328555320337
251 251 251^(1/2) + 1/50 251.6341191807102
252 252 6*7^(1/2) + 1/50 252.6353803146555
253 253 253^(1/2) + 1/50 253.6366389488234
254 254 254^(1/2) + 1/50 254.6378950980204
255 255 255^(1/2) + 1/50 255.6391487769068
256 256 801/50 256.6404000000000**
257 257 257^(1/2) + 1/50 257.6416487816753
258 258 258^(1/2) + 1/50 258.6428951361683
259 259 259^(1/2) + 1/50 259.6441390775772
260 260 260^(1/2) + 1/50 260.6453806198638
261 261 3*29^(1/2) + 1/50 261.6466197768561
262 262 262^(1/2) + 1/50 262.6478565622496
263 263 263^(1/2) + 1/50 263.6490909896091
264 264 264^(1/2) + 1/50 264.6503230723709
265 265 265^(1/2) + 1/50 265.6515528238440
266 266 266^(1/2) + 1/50 266.6527802572120
267 267 267^(1/2) + 1/50 267.6540053855347
268 268 268^(1/2) + 1/50 268.6552282217498
269 269 269^(1/2) + 1/50 269.6564487786743
270 270 3*30^(1/2) + 1/50 270.6576670690062
271 271 271^(1/2) + 1/50 271.6588831053262
272 272 4*17^(1/2) + 1/50 272.6600969000988
273 273 273^(1/2) + 1/50 273.6613084656743
274 274 274^(1/2) + 1/50 274.6625178142899
275 275 5*11^(1/2) + 1/50 275.6637249580710
276 276 276^(1/2) + 1/50 276.6649299090334
277 277 277^(1/2) + 1/50 277.6661326790837
278 278 278^(1/2) + 1/50 278.6673332800212
279 279 3*31^(1/2) + 1/50 279.6685317235395
280 280 280^(1/2) + 1/50 280.6697280212272
281 281 281^(1/2) + 1/50 281.6709221845696
282 282 282^(1/2) + 1/50 282.6721142249498
283 283 283^(1/2) + 1/50 283.6733041536504
284 284 284^(1/2) + 1/50 284.6744919818541
285 285 285^(1/2) + 1/50 285.6756777206454
286 286 286^(1/2) + 1/50 286.6768613810115
287 287 287^(1/2) + 1/50 287.6780429738439
288 288 12*2^(1/2) + 1/50 288.6792225099392
289 289 851/50 289.6804000000000**
290 290 290^(1/2) + 1/50 290.6815754546371
291 291 291^(1/2) + 1/50 291.6827488843692
292 292 292^(1/2) + 1/50 292.6839202996254
293 293 293^(1/2) + 1/50 293.6850897107449
294 294 7*6^(1/2) + 1/50 294.6862571279792
295 295 295^(1/2) + 1/50 295.6874225614927
296 296 296^(1/2) + 1/50 296.6885860213634
297 297 3*33^(1/2) + 1/50 297.6897475175845
298 298 298^(1/2) + 1/50 298.6909070600652
299 299 299^(1/2) + 1/50 299.6920646586316
300 300 10*3^(1/2) + 1/50 300.6932203230274
301 301 301^(1/2) + 1/50 301.6943740629159
302 302 302^(1/2) + 1/50 302.6955258878793
303 303 303^(1/2) + 1/50 303.6966758074212
304 304 4*19^(1/2) + 1/50 304.6978238309666
305 305 305^(1/2) + 1/50 305.6989699678629
306 306 3*34^(1/2) + 1/50 306.7001142273815
307 307 307^(1/2) + 1/50 307.7012566187174
308 308 308^(1/2) + 1/50 308.7023971509914
309 309 309^(1/2) + 1/50 309.7035358332499
310 310 310^(1/2) + 1/50 310.7046726744663
311 311 311^(1/2) + 1/50 311.7058076835419
312 312 312^(1/2) + 1/50 312.7069408693063
313 313 313^(1/2) + 1/50 313.7080722405181
314 314 314^(1/2) + 1/50 314.7092018058667
315 315 3*35^(1/2) + 1/50 315.7103295739720
316 316 316^(1/2) + 1/50 316.7114555533852
317 317 317^(1/2) + 1/50 317.7125797525906
318 318 318^(1/2) + 1/50 318.7137021800050
319 319 319^(1/2) + 1/50 319.7148228439796
320 320 8*5^(1/2) + 1/50 320.7159417527999
321 321 321^(1/2) + 1/50 321.7170589146867
322 322 322^(1/2) + 1/50 322.7181743377971
323 323 323^(1/2) + 1/50 323.7192880302244
324 324 901/50 324.7204000000000**
325 325 5*13^(1/2) + 1/50 325.7215102550928
326 326 326^(1/2) + 1/50 326.7226188034107
327 327 327^(1/2) + 1/50 327.7237256528010
328 328 328^(1/2) + 1/50 328.7248308110510
329 329 329^(1/2) + 1/50 329.7259342858886
330 330 330^(1/2) + 1/50 330.7270360849834
331 331 331^(1/2) + 1/50 331.7281362159464
332 332 332^(1/2) + 1/50 332.7292346863316
333 333 3*37^(1/2) + 1/50 333.7303315036357
334 334 334^(1/2) + 1/50 334.7314266752999
335 335 335^(1/2) + 1/50 335.7325202087089
336 336 4*21^(1/2) + 1/50 336.7336121111929
337 337 337^(1/2) + 1/50 337.7347023900275
338 338 13*2^(1/2) + 1/50 338.7357910524341
339 339 339^(1/2) + 1/50 339.7368781055808
340 340 340^(1/2) + 1/50 340.7379635565834
341 341 341^(1/2) + 1/50 341.7390474125048
342 342 3*38^(1/2) + 1/50 342.7401296803562
343 343 7*7^(1/2) + 1/50 343.7412103670981
344 344 344^(1/2) + 1/50 344.7422894796397
345 345 345^(1/2) + 1/50 345.7433670248402
346 346 346^(1/2) + 1/50 346.7444430095096
347 347 347^(1/2) + 1/50 347.7455174404079
348 348 348^(1/2) + 1/50 348.7465903242471
349 349 349^(1/2) + 1/50 349.7476616676908
350 350 5*14^(1/2) + 1/50 350.7487314773548
351 351 3*39^(1/2) + 1/50 351.7497997598078
352 352 4*22^(1/2) + 1/50 352.7508665215718
353 353 353^(1/2) + 1/50 353.7519317691222
354 354 354^(1/2) + 1/50 354.7529955088891
355 355 355^(1/2) + 1/50 355.7540577472567
356 356 356^(1/2) + 1/50 356.7551184905645
357 357 357^(1/2) + 1/50 357.7561777451077
358 358 358^(1/2) + 1/50 358.7572355171370
359 359 359^(1/2) + 1/50 359.7582918128598
360 360 6*10^(1/2) + 1/50 360.7593466384404
361 361 951/50 361.7604000000000**
362 362 362^(1/2) + 1/50 362.7614519036175
363 363 11*3^(1/2) + 1/50 363.7625023553302
364 364 364^(1/2) + 1/50 364.7635513611335
365 365 365^(1/2) + 1/50 365.7645989269816
366 366 366^(1/2) + 1/50 366.7656450587884
367 367 367^(1/2) + 1/50 367.7666897624267
368 368 4*23^(1/2) + 1/50 368.7677330437299
369 369 3*41^(1/2) + 1/50 369.7687749084919
370 370 370^(1/2) + 1/50 370.7698153624668
371 371 371^(1/2) + 1/50 371.7708544113704
372 372 372^(1/2) + 1/50 372.7718920608794
373 373 373^(1/2) + 1/50 373.7729283166331
374 374 374^(1/2) + 1/50 374.7739631842325
375 375 5*15^(1/2) + 1/50 375.7749966692414
376 376 376^(1/2) + 1/50 376.7760287771866
377 377 377^(1/2) + 1/50 377.7770595135579
378 378 3*42^(1/2) + 1/50 378.7780888838089
379 379 379^(1/2) + 1/50 379.7791168933572
380 380 380^(1/2) + 1/50 380.7801435475847
381 381 381^(1/2) + 1/50 381.7811688518378
382 382 382^(1/2) + 1/50 382.7821928114277
383 383 383^(1/2) + 1/50 383.7832154316312
384 384 8*6^(1/2) + 1/50 384.7842367176905
385 385 385^(1/2) + 1/50 385.7852566748139
386 386 386^(1/2) + 1/50 386.7862753081754
387 387 3*43^(1/2) + 1/50 387.7872926229162
388 388 388^(1/2) + 1/50 388.7883086241436
389 389 389^(1/2) + 1/50 389.7893233169327
390 390 390^(1/2) + 1/50 390.7903367063252
391 391 391^(1/2) + 1/50 391.7913487973314
392 392 14*2^(1/2) + 1/50 392.7923595949289
393 393 393^(1/2) + 1/50 393.7933691040640
394 394 394^(1/2) + 1/50 394.7943773296511
395 395 395^(1/2) + 1/50 395.7953842765741
396 396 6*11^(1/2) + 1/50 396.7963899496852
397 397 397^(1/2) + 1/50 397.7973943538069
398 398 398^(1/2) + 1/50 398.7983974937304
399 399 399^(1/2) + 1/50 399.7993993742174
400 400 1001/50 400.8004000000000**
401 401 401^(1/2) + 1/50 401.8013993757801
402 402 402^(1/2) + 1/50 402.8023975062305
403 403 403^(1/2) + 1/50 403.8033943959954
404 404 404^(1/2) + 1/50 404.8043900496896
405 405 9*5^(1/2) + 1/50 405.8053844719000
406 406 406^(1/2) + 1/50 406.8063776671844
407 407 407^(1/2) + 1/50 407.8073696400733
408 408 408^(1/2) + 1/50 408.8083603950689
409 409 409^(1/2) + 1/50 409.8093499366462
410 410 410^(1/2) + 1/50 410.8103382692527
411 411 411^(1/2) + 1/50 411.8113253973086
412 412 412^(1/2) + 1/50 412.8123113252073
413 413 413^(1/2) + 1/50 413.8132960573161
414 414 3*46^(1/2) + 1/50 414.8142795979750
415 415 415^(1/2) + 1/50 415.8152619514984
416 416 4*26^(1/2) + 1/50 416.8162431221748
417 417 417^(1/2) + 1/50 417.8172231142665
418 418 418^(1/2) + 1/50 418.8182019320104
419 419 419^(1/2) + 1/50 419.8191795796183
420 420 420^(1/2) + 1/50 420.8201560612767
421 421 421^(1/2) + 1/50 421.8211313811474
422 422 422^(1/2) + 1/50 422.8221055433670
423 423 3*47^(1/2) + 1/50 423.8230785520480
424 424 424^(1/2) + 1/50 424.8240504112790
425 425 5*17^(1/2) + 1/50 425.8250211251236
426 426 426^(1/2) + 1/50 426.8259906976220
427 427 427^(1/2) + 1/50 427.8269591327909
428 428 428^(1/2) + 1/50 428.8279264346231
429 429 429^(1/2) + 1/50 429.8288926070883
430 430 430^(1/2) + 1/50 430.8298576541330
431 431 431^(1/2) + 1/50 431.8308215796811
432 432 12*3^(1/2) + 1/50 432.8317843876331
433 433 433^(1/2) + 1/50 433.8327460818674
434 434 434^(1/2) + 1/50 434.8337066662400
435 435 435^(1/2) + 1/50 435.8346661445846
436 436 436^(1/2) + 1/50 436.8356245207129
437 437 437^(1/2) + 1/50 437.8365817984147
438 438 438^(1/2) + 1/50 438.8375379814582
439 439 439^(1/2) + 1/50 439.8384930735903
440 440 440^(1/2) + 1/50 440.8394470785361
441 441 1051/50 441.8404000000000**
442 442 442^(1/2) + 1/50 442.8413518416652
443 443 443^(1/2) + 1/50 443.8423026071939
444 444 444^(1/2) + 1/50 444.8432523002281
445 445 445^(1/2) + 1/50 445.8442009243892
446 446 446^(1/2) + 1/50 446.8451484832776
447 447 447^(1/2) + 1/50 447.8460949804746
448 448 8*7^(1/2) + 1/50 448.8470404195407
449 449 449^(1/2) + 1/50 449.8479848040167
450 450 15*2^(1/2) + 1/50 450.8489281374239
451 451 451^(1/2) + 1/50 451.8498704232638
452 452 452^(1/2) + 1/50 452.8508116650188
453 453 453^(1/2) + 1/50 453.8517518661517
454 454 454^(1/2) + 1/50 454.8526910301065
455 455 455^(1/2) + 1/50 455.8536291603081
456 456 456^(1/2) + 1/50 456.8545662601625
457 457 457^(1/2) + 1/50 457.8555023330572
458 458 458^(1/2) + 1/50 458.8564373823612
459 459 3*51^(1/2) + 1/50 459.8573714114251
460 460 460^(1/2) + 1/50 460.8583044235810
461 461 461^(1/2) + 1/50 461.8592364221433
462 462 462^(1/2) + 1/50 462.8601674104082
463 463 463^(1/2) + 1/50 463.8610973916540
464 464 4*29^(1/2) + 1/50 464.8620263691415
465 465 465^(1/2) + 1/50 465.8629543461138
466 466 466^(1/2) + 1/50 466.8638813257969
467 467 467^(1/2) + 1/50 467.8648073113990
468 468 6*13^(1/2) + 1/50 468.8657323061113
469 469 469^(1/2) + 1/50 469.8666563131083
470 470 470^(1/2) + 1/50 470.8675793355472
471 471 471^(1/2) + 1/50 471.8685013765685
472 472 472^(1/2) + 1/50 472.8694224392960
473 473 473^(1/2) + 1/50 473.8703425268373
474 474 474^(1/2) + 1/50 474.8712616422830
475 475 5*19^(1/2) + 1/50 475.8721797887082
476 476 476^(1/2) + 1/50 476.8730969691708
477 477 3*53^(1/2) + 1/50 477.8740131867136
478 478 478^(1/2) + 1/50 478.8749284443630
479 479 479^(1/2) + 1/50 479.8758427451296
480 480 4*30^(1/2) + 1/50 480.8767560920082
481 481 481^(1/2) + 1/50 481.8776684879784
482 482 482^(1/2) + 1/50 482.8785799360040
483 483 483^(1/2) + 1/50 483.8794904390334
484 484 1101/50 484.8804000000000**
485 485 485^(1/2) + 1/50 485.8813086218217
486 486 9*6^(1/2) + 1/50 486.8822163074019
487 487 487^(1/2) + 1/50 487.8831230596285
488 488 488^(1/2) + 1/50 488.8840288813750
489 489 489^(1/2) + 1/50 489.8849337754999
490 490 7*10^(1/2) + 1/50 490.8858377448473
491 491 491^(1/2) + 1/50 491.8867407922464
492 492 492^(1/2) + 1/50 492.8876429205128
493 493 493^(1/2) + 1/50 493.8885441324470
494 494 494^(1/2) + 1/50 494.8894444308357
495 495 3*55^(1/2) + 1/50 495.8903438184515
496 496 4*31^(1/2) + 1/50 496.8912422980527
497 497 497^(1/2) + 1/50 497.8921398723843
498 498 498^(1/2) + 1/50 498.8930365441768
499 499 499^(1/2) + 1/50 499.8939323161475
500 500 10*5^(1/2) + 1/50 500.8948271909999
501 501 501^(1/2) + 1/50 501.8957211714240
502 502 502^(1/2) + 1/50 502.8966142600963
503 503 503^(1/2) + 1/50 503.8975064596802
504 504 6*14^(1/2) + 1/50 504.8983977728258
505 505 505^(1/2) + 1/50 505.8992882021697
506 506 506^(1/2) + 1/50 506.9001777503361
507 507 13*3^(1/2) + 1/50 507.9010664199357
508 508 508^(1/2) + 1/50 508.9019542135667
509 509 509^(1/2) + 1/50 509.9028411338143
510 510 510^(1/2) + 1/50 510.9037271832509
511 511 511^(1/2) + 1/50 511.9046123644365
512 512 16*2^(1/2) + 1/50 512.9054966799189
513 513 3*57^(1/2) + 1/50 513.9063801322325
514 514 514^(1/2) + 1/50 514.9072627239004
515 515 515^(1/2) + 1/50 515.9081444574327
516 516 516^(1/2) + 1/50 516.9090253353280
517 517 517^(1/2) + 1/50 517.9099053600721
518 518 518^(1/2) + 1/50 518.9107845341392
519 519 519^(1/2) + 1/50 519.9116628599916
520 520 520^(1/2) + 1/50 520.9125403400792
521 521 521^(1/2) + 1/50 521.9134169768409
522 522 3*58^(1/2) + 1/50 522.9142927727037
523 523 523^(1/2) + 1/50 523.9151677300823
524 524 524^(1/2) + 1/50 524.9160418513808
525 525 5*21^(1/2) + 1/50 525.9169151389910
526 526 526^(1/2) + 1/50 526.9177875952943
527 527 527^(1/2) + 1/50 527.9186592226599
528 528 4*33^(1/2) + 1/50 528.9195300234461
529 529 1151/50 529.9204000000000**
530 530 530^(1/2) + 1/50 530.9212691546577
531 531 3*59^(1/2) + 1/50 531.9221374897442
532 532 532^(1/2) + 1/50 532.9230050075737
533 533 533^(1/2) + 1/50 533.9238717104492
534 534 534^(1/2) + 1/50 534.9247376006633
535 535 535^(1/2) + 1/50 535.9256026804976
536 536 536^(1/2) + 1/50 536.9264669522232
537 537 537^(1/2) + 1/50 537.9273304181005
538 538 538^(1/2) + 1/50 538.9281930803794
539 539 7*11^(1/2) + 1/50 539.9290549412996
540 540 6*15^(1/2) + 1/50 540.9299160030898
541 541 541^(1/2) + 1/50 541.9307762679691
542 542 542^(1/2) + 1/50 542.9316357381458
543 543 543^(1/2) + 1/50 543.9324944158185
544 544 4*34^(1/2) + 1/50 544.9333523031753
545 545 545^(1/2) + 1/50 545.9342094023943
546 546 546^(1/2) + 1/50 546.9350657156439
547 547 547^(1/2) + 1/50 547.9359212450821
548 548 548^(1/2) + 1/50 548.9367759928576
549 549 3*61^(1/2) + 1/50 549.9376299611088
550 550 5*22^(1/2) + 1/50 550.9384831519648
551 551 551^(1/2) + 1/50 551.9393355675444
552 552 552^(1/2) + 1/50 552.9401872099576
553 553 553^(1/2) + 1/50 553.9410380813043
554 554 554^(1/2) + 1/50 554.9418881836751
555 555 555^(1/2) + 1/50 555.9427375191513
556 556 556^(1/2) + 1/50 556.9435860898041
557 557 557^(1/2) + 1/50 557.9444338976965
558 558 3*62^(1/2) + 1/50 558.9452809448815
559 559 559^(1/2) + 1/50 559.9461272334029
560 560 4*35^(1/2) + 1/50 560.9469727652960
561 561 561^(1/2) + 1/50 561.9478175425861
562 562 562^(1/2) + 1/50 562.9486615672903
563 563 563^(1/2) + 1/50 563.9495048414165
564 564 564^(1/2) + 1/50 564.9503473669630
565 565 565^(1/2) + 1/50 565.9511891459204
566 566 566^(1/2) + 1/50 566.9520301802695
567 567 9*7^(1/2) + 1/50 567.9528704719833
568 568 568^(1/2) + 1/50 568.9537100230250
569 569 569^(1/2) + 1/50 569.9545488353501
570 570 570^(1/2) + 1/50 570.9553869109051
571 571 571^(1/2) + 1/50 571.9562242516279
572 572 572^(1/2) + 1/50 572.9570608594481
573 573 573^(1/2) + 1/50 573.9578967362869
574 574 574^(1/2) + 1/50 574.9587318840568
575 575 5*23^(1/2) + 1/50 575.9595663046625
576 576 1201/50 576.9603999999999**
577 577 577^(1/2) + 1/50 577.9612329719571
578 578 17*2^(1/2) + 1/50 578.9620652224138
579 579 579^(1/2) + 1/50 579.9628967532414
580 580 580^(1/2) + 1/50 580.9637275663034
581 581 581^(1/2) + 1/50 581.9645576634556
582 582 582^(1/2) + 1/50 582.9653870465452
583 583 583^(1/2) + 1/50 583.9662157174121
584 584 584^(1/2) + 1/50 584.9670436778875
585 585 3*65^(1/2) + 1/50 585.9678709297957
586 586 586^(1/2) + 1/50 586.9686974749528
587 587 587^(1/2) + 1/50 587.9695233151668
588 588 14*3^(1/2) + 1/50 588.9703484522386
589 589 589^(1/2) + 1/50 589.9711728879608
590 590 590^(1/2) + 1/50 590.9719966241192
591 591 591^(1/2) + 1/50 591.9728196624915
592 592 4*37^(1/2) + 1/50 592.9736420048476
593 593 593^(1/2) + 1/50 593.9744636529509
594 594 3*66^(1/2) + 1/50 594.9752846085563
595 595 595^(1/2) + 1/50 595.9761048734121
596 596 596^(1/2) + 1/50 596.9769244492586
597 597 597^(1/2) + 1/50 597.9777433378296
598 598 598^(1/2) + 1/50 598.9785615408509
599 599 599^(1/2) + 1/50 599.9793790600415
600 600 10*6^(1/2) + 1/50 600.9801958971133
601 601 601^(1/2) + 1/50 601.9810120537704
602 602 602^(1/2) + 1/50 602.9818275317108
603 603 3*67^(1/2) + 1/50 603.9826423326247
604 604 604^(1/2) + 1/50 604.9834564581955
605 605 11*5^(1/2) + 1/50 605.9842699100999
606 606 606^(1/2) + 1/50 606.9850826900073
607 607 607^(1/2) + 1/50 607.9858947995804
608 608 4*38^(1/2) + 1/50 608.9867062404750
609 609 609^(1/2) + 1/50 609.9875170143403
610 610 610^(1/2) + 1/50 610.9883271228182
611 611 611^(1/2) + 1/50 611.9891365675446
612 612 6*17^(1/2) + 1/50 612.9899453501481
613 613 613^(1/2) + 1/50 613.9907534722512
614 614 614^(1/2) + 1/50 614.9915609354690
615 615 615^(1/2) + 1/50 615.9923677414110
616 616 616^(1/2) + 1/50 616.9931738916792
617 617 617^(1/2) + 1/50 617.9939793878700
618 618 618^(1/2) + 1/50 618.9947842315725
619 619 619^(1/2) + 1/50 619.9955884243700
620 620 620^(1/2) + 1/50 620.9963919678391
621 621 3*69^(1/2) + 1/50 621.9971948635502
622 622 622^(1/2) + 1/50 622.9979971130672
623 623 623^(1/2) + 1/50 623.9987987179478
624 624 4*39^(1/2) + 1/50 624.9995996797437
625 626 1251/50 626.0004000000000**x
626 627 626^(1/2) + 1/50 627.0011996802557x
627 628 627^(1/2) + 1/50 628.0019987220439x
625 26
Cases at bottom marked with x do not have the needed floor.
** marks all the rational solutions.
The numbers at the bottom show there are 625 solutions, 25 of which are rational (26 is the count that includes the solution 626.0004, which does not match the 625 floor sought).
clearvars,clc
syms x
fplot(@(x)(x-1/50)^2-floor(x^2))
grid;
ct=0; ct2=0;
for i=sym(0):sym(25)^2+2;
eq=(x-1/sym(50))^2==i;
s=solve(eq,x);
xv=eval(s(2));
fx=floor(xv^2);
fprintf('%4d %4d %-19s %19.13f',i,fx,s(2),xv^2)
sx=string(s(2));
ix=strfind(sx,"^(");
if isempty(ix)
ct2=ct2+1;
fprintf('**')
end
if i~=fx
fprintf('x')
else
ct=ct+1;
end
fprintf('\n')
end
disp([ct ct2])
|
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Posted by Charlie
on 2023-04-03 09:03:53 |
computer solution
