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Find the lowest n (Posted on 2015-06-22) Difficulty: 3 of 5
Are there distinct positive integers a,b,n for which:
1/n = 1/a^2+1/b^2,
?

If so, find the triplet with lowest n.

No Solution Yet Submitted by Ady TZIDON    
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re: A few other n | Comment 3 of 4 |
(In reply to A few other n by Steve Herman)

a   b   n
5 10 20
10 20 80
15 20 144
10 30 90
15 30 180
20 40 320
26 39 468
30 40 576
25 50 500
10 70 98
20 60 360
17 68 272
30 60 720
35 70 980
45 60 1296
30 90 810
40 80 1280
52 78 1872
45 90 1620
60 80 2304
50 100 2000
26 130 650
20 140 392
40 120 1440
55 110 2420
34 136 1088
75 100 3600
60 120 2880
65 130 3380
78 117 4212
50 150 2250
58 145 2900
70 140 3920
90 120 5184
65 156 3600
75 150 4500
30 210 882
60 180 3240
80 160 5120
105 140 7056
51 204 2448
85 170 5780
37 222 1332
104 156 7488
90 180 6480
102 170 7650
70 210 4410
120 160 9216
95 190 7220
100 200 8000
52 260 2600
105 210 8820
135 180 11664
40 280 1568
80 240 5760
50 275 2420
130 195 11700
110 220 9680
68 272 4352
115 230 10580
150 200 14400
90 270 7290
120 240 11520
164 205 16400
125 250 12500
165 220 17424
130 260 13520
156 234 16848
136 255 14400
50 350 2450
100 300 9000
135 270 14580
116 290 11600
140 280 15680
180 240 20736
85 340 6800
145 290 16820
110 330 10890
130 312 14400
150 300 18000
182 273 22932
195 260 24336
155 310 19220
78 390 5850
106 371 10388
60 420 3528
120 360 12960
160 320 20480
210 280 28224
165 330 21780
102 408 9792
170 340 23120
74 444 5328
130 390 15210
208 312 29952
175 350 24500
225 300 32400
180 360 25920
204 340 30600
185 370 27380
70 490 4802
140 420 17640
240 320 36864
190 380 28880
174 406 25578
65 520 4160
195 390 30420
234 351 37908
119 476 13328
255 340 41616
150 450 20250
200 400 32000
174 435 26100
205 410 33620
104 520 10400
182 442 28322
210 420 35280
270 360 46656
80 560 6272
160 480 23040
215 430 36980
100 550 9680
260 390 46800
220 440 38720
195 468 32400
285 380 51984
305 366 54900
225 450 40500
136 544 17408
170 510 26010
230 460 42320
300 400 57600
235 470 44180
260 455 50960
286 429 56628
90 630 7938
180 540 29160
240 480 46080
245 490 48020
315 420 63504
328 410 65600
250 500 50000
190 570 32490
153 612 22032
255 510 52020
330 440 69696
175 600 28224
111 666 11988
130 650 16250
260 520 54080
312 468 67392
272 510 57600
265 530 56180
100 700 9800
200 600 36000
219 584 42048
345 460 76176
270 540 58320
232 580 46400
306 510 68850
82 738 6642
275 550 60500
210 630 39690
280 560 62720
360 480 82944
338 507 79092
170 680 27200
285 570 64980
290 580 67280
375 500 90000
110 770 11858
220 660 43560
260 624 57600
295 590 69620
370 518 90650
300 600 72000
364 546 91728
390 520 97344
305 610 74420
230 690 47610
310 620 76880
170 765 27540
187 748 32912
156 780 23400
315 630 79380
405 540 104976
212 742 41552
120 840 14112
240 720 51840
320 640 81920
150 825 21780
325 650 84500
390 585 105300
420 560 112896
330 660 87120
250 750 56250

from

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For tot = 3 To 1000
  For a = 1 To tot / 2
    b = tot - a
    If b > a Then
        t = 1 / (a * a) + 1 / (b * b)
        n = 1 / t
        nr = Int(n + 0.5)
        If Abs(n - nr) < 0.0000001 Then
          Text1.Text = Text1.Text & a & Str(b) & Str(n) & crlf
          DoEvents
        End If
    End If
  Next
 Next
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2015-06-23 07:24:20
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