Jsun Yui Wong

The computer program listed below seeks to solve the Lander *et al.* 1967/Ekl 1998 Diophantine equation in Weisstein [96, Expression 14]:

4 * X(1) ^ 9 + 2 * X(2) ^ 9 + X(3) ^ 9 + X(4) ^ 9 + X(5) ^ 9 + X(6) ^ 9 + 2 * X(7) ^ 9 = X(8) ^ 9 + X(9) ^ 9

where X(1) through X(9) 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 32000

83 RANDOMIZE JJJJ

87 M = -4E+299

120 FOR J44 = 1 TO 9

121 A(J44) = 1 + FIX(RND * 20)

122 NEXT J44

128 FOR I = 0 TO FIX(RND * 150000)

129 FOR KKQQ = 1 TO 9

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

135 FOR IPP = 1 TO FIX(1 + RND * 3.3)

143 j = 1 + FIX(RND * 9)

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 9

173 REM X(J44) = INT(X(J44))

174 IF X(J44) < 1 THEN 1670

175 NEXT J44

1123 P = -ABS(4 * X(1) ^ 9## + 2 * X(2) ^ 9## + X(3) ^ 9## + X(4) ^ 9## + X(5) ^ 9## + X(6) ^ 9## + 2 * X(7) ^ 9## - X(8) ^ 9## - X(9) ^ 9##)

1127 IF P <= M THEN 1670

1420 M = P

1444 FOR KLX = 1 TO 9

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1557 GOTO 128

1670 NEXT I

1894 IF M < -5 THEN 1999

1923 PRINT A(1), A(2), A(3), A(4), A(5)

1924 PRINT A(1) ^ 9##, A(2) ^ 9##, A(3) ^ 9##, A(4) ^ 9##, A(5) ^ 9##

1925 PRINT A(6), A(7), A(8), A(9), M, JJJJ

1927 PRINT A(6) ^ 9#, A(7) ^ 9##, A(8) ^ 9##, A(9) ^ 9##, M ^ 9##, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [97]. The complete output of a single run through JJJJ= -27010 is shown below:

2 19 16 4 17

512 322687697779 68719476736 262144

118587876497

7 3 21 15 0

-28130

40353607 19683 794280046581 38443359375

0 -28130

2 3 17 4 16

512 19683 118587876497 262144

68719476736

7 19 15 21 0

-27010

40353607 322687697779 38443359375 794280046581

0 -27010

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 = -27010 took 10 minutes. One can compare the computational results above with the Lander *et al.* 1967/Ekl 1998 solution given in Weisstein [96], Expression (14).

**Acknowledgment**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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