Jsun Yui Wong
The computer program listed below seeks to solve the Lander et al. 1967 Diophantine equation in Weisstein [95, Expression 52]:
3 * X(11) ^ 10 + X(12) ^ 10 = 5 * X(1) ^ 10 + 2 * X(2) ^ 10 + 2 * X(3) ^ 10 + X(4) ^ 10 + 4 * X(5) ^ 10 + 3 * X(6) ^ 10 + X(7) ^ 10 + 2 * X(8) ^ 10 + 2 * X(9) ^ 10 + X(10) ^ 10 where X(1) through X(12) are general integer variables--X(i)=1, 2, 3, ....
0 DEFDBL A-Z
1 DEFINT K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)
81 FOR JJJJ = -32000 TO 632000
83 RANDOMIZE JJJJ
87 M = -4E+299
120 FOR J44 = 1 TO 10
121 A(J44) = 2 + FIX(RND * 13)
123 NEXT J44
124 A(11) = 10 + FIX(RND * 4)
126 A(12) = 10 + FIX(RND * 8)
128 FOR I = 0 TO FIX(RND * 50000)
129 FOR KKQQ = 1 TO 12
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 3.3)
143 j = 1 + FIX(RND * 12)
162 IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 3.3) ELSE X(j) = A(j) + FIX(1 + RND * 3.3)
169 NEXT IPP
171 FOR J44 = 1 TO 12
173 REM X(J44) = INT(X(J44))
174 IF X(J44) < 1 THEN 1670
175 NEXT J44
1125 P = -ABS(-3 * X(11) ^ 10## - X(12) ^ 10## + 5 * X(1) ^ 10## + 2 * X(2) ^ 10## + 2 * X(3) ^ 10## + X(4) ^ 10## + 4 * X(5) ^ 10## + 3 * X(6) ^ 10## + X(7) ^ 10## + 2 * X(8) ^ 10## + 2 * X(9) ^ 10## + X(10) ^ 10##)
1127 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 12
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1894 IF M < -18 THEN 1999
1923 PRINT A(1), A(2), A(3), A(4), A(5)
1925 PRINT A(6), A(7), A(8), A(9), A(10), A(11), A(12), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [97]. The complete output of a single run through JJJJ= 8879 is shown below:
1 2 8 6 8
4 7 8 10 8
10 5 -3 -9100
1 2 10 4 6
7 8 3 14 15
11 16 0 -4333
1 8 2 8 8
4 7 8 10 6
10 5 -3 -1167
1 10 3 8 6
7 15 14 2 4
11 16 0 8879
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel (R) Core (TM) 2 Duo CPU E8400 @ 3.0 GHz 3.0 GHz, 4.00 GB of RAM (3.9 GB usable), 64-bit Operating System, and QB64v1000-win [97], the wall-clock time (not CPU time) for obtaining the output through JJJJ = 8879 took 45 minutes. One can compare the computational results above with the Lander et al. 1967 solution given in Weisstein [95], Expression (52).
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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