Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
The table below is seriously impressive in one respect: the program that generated it contained threenested loops each going to 1000. Counting the power calculations and primalitychecks, the program easily ran to several billion calculations. It ran in lessthan ten minutes on a not very state of the art desktop computer. Consideringthat I can remember when computer speeds were measured in kilohertz andlarge files in kilobytes, I find this impressive. And yes, the listing did stopat a = 846. In fact, when a is small, the quartets often stop with b and cvalues well short of 1000. Although quartet terms aren't as nearly equal in sizeas Pythagorean triplets, there do seem to be limits to the disparities in terms.
1 6 8 9 1 71 138 144 1 135 138 172 1 236 1207 1210 1 242 720 729 1 372 426 505 1 426 486 577 1 566 823 904 1 575 2292 2304 1 791 812 1010 1 1124 5610 5625 1 1851 8675 8703 1 1938 2820 3097 1 1943 6702 6756 1 1943 11646 11664 1 2196 5984 6081 1 2676 3230 3753 1 3086 21588 21609 1 3318 16806 16849 1 3453 24965 24987 1 4607 36840 36864 1 6560 59022 59049 1 7251 49409 49461 1 7676 11903 12884 1 8999 89970 90000 1 10230 37887 38134 1 10866 17328 18649 1 15218 66198 66465 1 17328 27630 29737 1 17384 78244 78529 1 25765 33857 38239 1 28182 31212 37513 1 29196 66167 68010 1 31212 34566 41545 1 32882 69479 71852 1 34199 46212 51762 1 51293 64165 73627 1 54101 56503 69709 1 58462 87383 95356 1 75263 94904 108608 1 84507 89559 109747 2 17 40 41 2 514 947 995 2 601 2831 2840 2 1987 2526 2883 2 8297 10303 11852 2 8703 19806 20351 2 9175 61049 61118 2 10447 17217 18414 2 10641 18808 19881 2 12925 14636 17429 2 17 40 41 2 514 947 995 2 601 2831 2840 2 1987 2526 2883 2 8297 10303 11852 2 8703 19806 20351 2 9175 61049 61118 2 10447 17217 18414 2 10641 18808 19881 2 12925 14636 17429 2 13867 25380 26691 2 14399 26089 27476 2 14481 21076 23145 2 16947 55221 55748 2 17800 20097 23961 2 18903 29806 32151 2 19063 60968 61583 2 20729 45064 46481 2 35302 44497 50929 3 4 5 6 3 10 18 19 3 34 114 115 3 36 37 46 3 121 131 159 3 214 309 340 3 245 340 378 3 509 1156 1188 3 632 1533 1568 3 695 7479 7481 3 1228 2325 2434 3 1485 1954 2206 3 1936 3005 3252 3 2459 3735 4061 3 4380 4622 5675 3 6180 17872 18115 3 11733 21220 22354 3 15859 68039 68325 3 16284 41989 42790 3 17445 43013 43949 3 18922 24381 27706 3 19504 90494 90795 3 22618 48248 49851 3 24645 34330 38128 3 26933 27670 34404 3 28820 42789 46766 3 42546 46144 55963 3 45369 62303 69467 3 84261 94124 112718 4 17 22 25 4 57 248 249 4 303 482 519 4 383 1438 1447 4 963 972 1219 4 1269 3155 3222 4 1329 1607 1866 4 1418 1587 1899 4 1473 32639 32640 4 2198 2555 3011 4 2219 7965 8022 4 2345 3927 4188 4 3043 11006 11083 4
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