Jsun Yui Wong

The computer program listed below is about the following quotation from Sleziak [8]:

"Do there exist integers x, y, z, w that satisfy

(x+1)^2+y^2=(x+2)^2+z^2

(x+2)^2+z^2=(x+3)^2+w^2?"

0 DEFDBL A-Z

3 DEFINT J, K, X

4 DIM X(342), A(342), L(333), K(333)

12 FOR JJJJ = -32000 TO 32000

14 RANDOMIZE JJJJ

16 M = -1D+317

91 FOR KK = 91 TO 99

94 A(KK) = -75 + FIX(RND * 150)

95 NEXT KK

128 FOR I = 1 TO 8000

129 FOR K = 91 TO 99

131 X(K) = A(K)

132 NEXT K

155 FOR IPP = 1 TO FIX(1 + RND * 3)

181 B = 91 + FIX(RND * 9)

182 IF RND < -.1 THEN 183 ELSE GOTO 189

183 R = (1 - RND * 2) * A(B)

186 X(B) = A(B) + (RND ^ 3) * R

188 GOTO 191

189 IF RND < .5 THEN X(B) = A(B) - FIX(1 + RND * 1.99) ELSE X(B) = A(B) + FIX(1 + RND * 1.99)

191 NEXT IPP

335 N98 = (X(96) + 1) ^ 2 + X(97) ^ 2 - (X(96) + 2) ^ 2 - X(98) ^ 2

339 N99 = (X(96) + 2) ^ 2 + X(98) ^ 2 - (X(96) + 3) ^ 2 - X(99) ^ 2

1335 P = -ABS(N98) - ABS(N99)

1499 IF P <= M THEN 1670

1657 FOR KEW = 96 TO 99

1658 A(KEW) = X(KEW)

1659 NEXT KEW

1661 M = P

1670 NEXT I

1888 IF M < 0 THEN 1999

1917 PRINT A(96), A(97), A(98), A(99), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [9]. Copied by hand from the screen, the computer programâ€™s complete output through JJJJ=-30603 is shown below:

30 -12 9 -4 0

-30990

30 -12 9 4 0

-30913

-34 -4 9 12 0

-30809

2 -4 3 0 0

-30603

Above there is no rounding by hand; it is just straight copying by hand from the screen.

On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and with qb64v1000-win [9], the wall-clock time through

JJJJ=-30603 was one minute.

**Acknowledgment**

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

References

[1] R. Burden, J. Faires, A. Burden, *Numerical Analysis*, Tenth Edition. Cengage Learning, 2016.

[2] R. Burden, J. Faires, *Numerical Analysis*, Sixth Edition. Brooks/Cole Publishing Company, 1996.

[3] R. Burden, J. Faires, *Numerical Analysis*, Third Edition. PWS Publishers, 1985.

[4] D. Greenspan, V. Casulli,* Numerical Analysis for Applied Mathematics, Science, and Engineering*. Addison-Wesley Publishing Company, 1988

[5] L. W. Johnson, R. D. Riess, *Numerical Analysis*, Second Edition. Addison-Wesley Publishing Company, 1982

[6] Microsoft Corp. *BASIC*, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[7] William H. Mills, A System of Quadratic Diophantine Equations, *Pacific Journal of Mathematics*, 3 (1953), pp. 209-220.

[8] Martin Sleziak, Integer Solutions to Nonlinear System of Equations.... www.math.stackexchange.com/questions/2085253/integer-solutions-to-nonlinear-system-of-equations

[9] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.