Three 3-digit non leading zero positive base N integers
P,
Q
and
R, with
P >
Q >
R, are such that:
- Q is the geometric mean of P and R, and:
- P, Q and R can be derived from one another by
cyclic permutation of digits.
Determine all possible positive integer values of N < 30 for which this is possible.
(In reply to
computer solution for N<=100 by Charlie)
88 60 58 56 58 56 60 56 60 58 469800 454140 439002
88 67 4 16 16 67 4 4 67 4 519216 129804 32451
88 68 16 3 16 3 68 3 68 16 528003 124236 29232
91 31 30 29 30 29 31 29 31 30 259470 251100 243000
91 62 60 58 60 58 62 58 62 60 518940 502200 486000
92 77 2 12 12 77 2 2 77 2 651924 108654 18109
92 78 12 1 12 1 78 1 78 12 661297 101738 15652
92 88 30 51 51 88 30 30 88 30 747643 439790 258700
93 27 13 6 13 6 27 6 27 13 234738 113022 54418
93 53 13 26 26 53 13 13 53 13 459632 229816 114908
93 54 26 12 26 12 54 12 54 26 469476 226044 108836
93 81 39 18 39 18 81 18 81 39 704214 339066 163254
94 20 8 3 8 3 20 3 20 8 177475 70990 28396
94 22 7 2 7 2 22 2 22 7 195052 62062 19747
94 32 31 30 31 30 32 30 32 31 285696 276768 268119
94 40 16 6 16 6 40 6 40 16 354950 141980 56792
94 44 14 4 14 4 44 4 44 14 390104 124124 39494
94 59 10 24 24 59 10 10 59 10 522288 217620 90675
94 60 24 9 24 9 60 9 60 24 532425 212970 85188
94 64 62 60 62 60 64 60 64 62 571392 553536 536238
94 65 7 21 21 65 7 7 65 7 575019 191673 63891
94 66 21 6 21 6 66 6 66 21 585156 186186 59241
94 76 45 26 45 26 76 26 76 45 675792 400140 236925
94 80 32 12 32 12 80 12 80 32 709900 283960 113584
94 88 28 8 28 8 88 8 88 28 780208 248248 78988
95 53 14 27 27 53 14 14 53 14 479682 248724 128968
95 54 27 13 27 13 54 13 54 27 489928 244964 122482
96 14 4 1 4 1 14 1 14 4 129409 36974 10564
96 28 8 2 8 2 28 2 28 8 258818 73948 21128
96 42 12 3 12 3 42 3 42 12 388227 110922 31692
96 56 16 4 16 4 56 4 56 16 517636 147896 42256
96 69 6 20 20 69 6 6 69 6 636500 190950 57285
96 70 20 5 20 5 70 5 70 20 647045 184870 52820
96 80 28 47 47 80 28 28 80 28 740015 440860 262640
96 84 24 6 24 6 84 6 84 24 776454 221844 63384
97 33 32 31 32 31 33 31 33 32 313632 304128 294912
97 66 64 62 64 62 66 62 66 64 627264 608256 589824
98 79 3 15 15 79 3 3 79 3 759025 151805 30361
98 80 15 2 15 2 80 2 80 15 769792 144336 27063
100 34 33 32 33 32 34 32 34 33 343332 333234 323433
100 43 24 32 32 43 24 24 43 24 432432 324324 243243
100 44 32 23 32 23 44 23 44 32 443223 322344 234432
100 53 9 1 9 1 53 1 53 9 530901 90153 15309
100 57 14 28 28 57 14 14 57 14 571428 285714 142857
100 58 28 13 28 13 58 13 58 28 582813 281358 135828
100 64 2 11 11 64 2 2 64 2 640211 116402 21164
100 64 10 25 25 64 10 10 64 10 641025 256410 102564
100 65 25 9 25 9 65 9 65 25 652509 250965 96525
100 68 8 23 23 68 8 8 68 8 680823 236808 82368
100 68 66 64 66 64 68 64 68 66 686664 666468 646866
100 69 23 7 23 7 69 7 69 23 692307 230769 76923
100 75 5 19 19 75 5 5 75 5 750519 197505 51975
100 75 25 43 43 75 25 25 75 25 752543 437525 254375
100 76 19 4 19 4 76 4 76 19 761904 190476 47619
100 86 48 64 64 86 48 48 86 48 864864 648648 486486
100 86 53 32 53 32 86 32 86 53 865332 533286 328653
100 88 64 46 64 46 88 46 88 64 886446 644688 468864
100 89 1 9 9 89 1 1 89 88 890109 98901 10989
100 91 29 51 51 91 29 29 91 29 912951 519129 295191
100 94 76 61 76 61 94 61 94 76 947661 766194 619476
|
|
Posted by Charlie
on 2009-07-04 16:01:13 |
re: computer solution for N<=100 -- the rest of it
