A Computer Program for Solving Systems of Diophantine Nonlinear Equations, Part 2
Jsun Yui Wong
The computer program below seeks to solve simultaneously the system of three Diophantine equations taken from page 112 of Sierpinski [61]. His simultaneous equations are as follows: +X(1)^2 +X(2)^2 = X(4)^2
+X(1)^2 +X(3)^2 = X(5)^2
+X(2)^2 +X(3)^2 = X(6)^2
0 DEFDBL A-Z 1 DEFINT I,J,K,A,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+30 111 FOR J44=1 TO 6 112 A(J44)=50+ ( RND *1000) 113 NEXT J44 128 FOR I=1 TO 2000 129 FOR KKQQ=1 TO 6 130 X(KKQQ)=A(KKQQ) 131 NEXT KKQQ 139 FOR IPP=1 TO FIX(1+RND*3) 140 B=1+FIX(RND*6) 150 R=(1-RND*2)*A(B) 155 IF RND0 THEN PN(J44)=-1000000!*ABS(N(J44)) ELSE PN(J44)=0 203 NEXT J44 321 REM 322 PD1=-ABS(N(7))-ABS(N(8) )-ABS( N(9) ) 1111 IF PD1<=M THEN 1670 1452 M=PD1 1454 FOR KLX=1 TO 6 1455 A(KLX)=X(KLX) 1456 NEXT KLX 1557 GOTO 128 1670 NEXT I 1889 IF M<-8 THEN 1999 1904 PRINT A(1),A(2),A(3),A(4),A(5),A(6),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=-31910 is shown below. What follows is a hand copy from the computer-monitor screen; immediately below there is no rounding by hand.
160 792 231 808 281 825 0 -31975
492 0 656 492 820 656 0
-31972
176 1025 0 1040 176 1025 -1 -31966
157 1021 0 1033 157 1021 -1 -31951
0 168 576 168 576 600 0 -31932
0 340 189 340 189 389 0 -31910
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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