Jsun Yui Wong
The computer program below seeks to solve the Diophantine equation
X(1)^5+ X(2)^5 +X(3)^5 +X(4)^5 = X(5)^5 taken from Lander and Parkin [12, p. 1079] and Lander and Parkin [13, p.102].
0 DEFDBL A-Z
1 DEFINT I,J,K,X
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
110 FOR J44=1 TO 5
111 IF X(J44)<20 THEN X(J44)=20
112 A(J44)=20+FIX( RND*200)
113 NEXT J44
128 FOR I=1 TO 750
129 FOR KKQQ=1 TO 5
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*5)
150 R=(1-RND*2)*A(B)
155 IF RND<.5 THEN 160 ELSE 167
160 X(B)=(A(B) +RND^3*R)
165 GOTO 168
167 IF RND<.5 THEN X(B)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1)
168 NEXT IPP
212 FOR J44=1 TO 5
213 IF X(J44)<20 THEN X(J44)=20
217 NEXT J44
311 N(7)= X(1)^5#+ X(2)^5# +X(3)^5# +X(4)^5# -X(5)^5
322 PD1=-ABS(N(7))
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 5
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<0 THEN 1999
1904 PRINT A(1),A(2),A(3),A(4)
1917 PRINT A(5),M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. The complete output through JJJJ=32000 is showm below. What follows is a hand copy from the computer-monitor screen; immediately below there is no rounding by hand.
27 84 110 133
144 0 -30445
27 133 84 110
144 0 16325
133 27 110 84
144 0 27724
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output through JJJJ=32000 was 42 minutes.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[23] Wikipedia, Euler Brick. en.wikipedia.org/wiki/Euler_brick.
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