Jsun Yui Wong
The computer program listed below seeks to improve on the realized solutions of the preceding paper. One notes line 195 and line 211, which are 195 X(4) = INT(X(4)) and
211 X(1) = (-X(4) * X(2)) / X(3), respectively.
0 DEFDBL A-Z
1 DEFINT J, K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)
88 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
111 FOR J44 = 1 TO 4
112 A(J44) = -10 + RND * 20
115 NEXT J44
128 FOR I = 1 TO 10000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 3)
140 B = 1 + FIX(RND * 4)
150 R = (1 – RND * 2) * A(B)
160 X(B) = (A(B) + RND ^ 3 * R)
168 NEXT IPP
195 X(4) = INT(X(4))
198 X(3) = 2 – X(4)
210 IF X(3) = 0 THEN GOTO 1670
211 X(1) = (-X(4) * X(2)) / X(3)
215 REM N(6) = -ABS(X(3) * X(1) + X(4) * X(2))
216 N(7) = -ABS(X(3) * X(1) ^ 2 + X(4) * X(2) ^ 2 – 2 / 3)
217 N(8) = -ABS(X(3) * X(1) ^ 3 + X(4) * X(2) ^ 3)
322 PD1 = N(7) + N(8)
1111 IF PD1 <= M THEN 1670
1452 M = PD1
1454 FOR KLX = 1 TO 4
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -.000000001 THEN 1999
1904 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [18]. Copied by hand from the screen, the computer program’s complete output through JJJJ=-31918 is shown below:
.5773502691877946 -.5773502691877946 1
1 -4.228800415308903D-12 -31992
-.5773502691866187 -.5773502691866187 1
1 -6.944536525693712D-12 -31985
.5773502691915871 -.5773502691915871 1
1 -4.529397256564094D-12 -31974
.5773502692572973 -.5773502692572973 1
1 -1.562806386579997D-10 -31942
-.5773502691903677 .5773502691903677 1
1 -1.713410663350956D-12 -31939
-.5773502691900816 .5773502691900816 1
1 -1.052680729043964D-12 -31918
Above there is no rounding by hand; it is just straight copying by hand from the screen.
On a personal computer using a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and using qb64v1000-win [18], the wall-clock time for obtaining the output through JJJJ= -31918 was 11 seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.388.158&rep=rep1&type=pdf
[4] Martin Gardner (1979), Mathematical Games. Scientific American, 241 (3), Page 25.
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[12] Tito Piezas III, Euler Bricks and Quadruples. http://sites.google.com/site/tpiezas/0021
[13] Anton Schigur, Solving a System of Diophantine Equations. Mathematics Stack Exchange. http://math.stackexchange.com/questions/398364/solving-a-system-of-diophantine-equations.
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[17] Wikipedia, Euler Brick. en.wikipedia.org/wiki/Euler_brick.
[18] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
[19] Jsun Yui Wong (2014, February 8), Testing the Nonlinear Integer Programming Solver with Lander and Parkin’s Counterexample to Euler’s Conjecture on Sums of Like Powers. https://computerprogramsandresults.wordpress.com/2014/02/08/testing.
computerprogramsandresults 