Jsun Yui Wong
The computer program listed below seeks to solve the following nonlinear Diophantine equation from Oliveira [17, p. 55]:
X(1)^2+ X(2)^2+X(3)^2+...+X(39)^2=39000.
0 DEFDBL A-Z
3 DEFINT J, K
4 DIM X(32768), A(32768), P(32768), K(32768)
5 FOR JJJJ = -32000 TO 32000
14 RANDOMIZE JJJJ
16 M = -1D+50
91 FOR KK = 1 TO 39
94 A(KK) = FIX(1 + RND * 20)
95 NEXT KK
128 FOR I = 1 TO 5000 STEP 1
129 FOR K = 1 TO 39
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 39)
183 R = (1 - RND * 2) * A(B)
188 REM IF RND < .2 THEN X(B) = FIX(A(B) + RND * R) ELSE IF RND < .25 THEN X(B) = FIX(A(B) + RND ^ 3 * R) ELSE IF RND < .333 THEN X(B) = FIX(A(B) + RND ^ 5 * R) ELSE IF RND < .5 THEN X(B) = FIX(A(B) + RND ^ 7 * R) ELSE X(B) = FIX(A(B) + RND ^ 9 * R)
191 IF RND < .5 THEN X(B) = CINT(A(B) - 1) ELSE X(B) = CINT(A(B) + 1)
199 NEXT IPP
201 FOR J43 = 1 TO 39
203 IF X(J43) < 1 THEN 1670
207 NEXT J43
211 SUML = 0
221 FOR J44 = 1 TO 39
231 SUML = SUML + X(J44) ^ 2
251 NEXT J44
261 PZ = -ABS(SUML - 39000)
1111 P = PZ
1451 IF P <= M THEN 1670
1657 FOR KEW = 1 TO 39
1658 A(KEW) = X(KEW)
1659 NEXT KEW
1661 M = P
1670 NEXT I
1890 IF M < -99999 THEN 1999
1911 PRINT A(1), A(2), A(3), A(4), A(5)
1913 PRINT A(6), A(7), A(8), A(9)
1915 PRINT A(10), A(11), A(12), A(13)
1916 PRINT A(14), A(15), A(16), A(17), A(18)
1917 PRINT A(19), A(20), A(21), A(22), A(23)
1918 PRINT A(24), A(25), A(26), A(27), A(28)
1919 PRINT A(29), A(30), A(31), A(32), A(33)
1920 PRINT A(34), A(35)
1925 PRINT A(36), A(37), A(38), A(39), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [20]. Copied by hand from the screen, the computer program’s complete output through JJJJ= -31999 is shown below.
23 31 45 22 26
30 35 55 15
51 33 30 44
31 6 27 40 6
7 16 11 47 14
42 25 14 51 48
25 35 43 43 12
43 15
3 22 11 19 0
-32000
40 49 43 51 35
31 27 31 11
14 35 36 24
30 12 15 42 27
18 37 35 9 17
42 26 26 21 25
6 44 56 36 46
17 29
30 26 15 24 0
-31999
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 [20], the wall-clock time for obtaining the output through JJJJ= -31999 was two seconds, not including "Creating .EXE file..." time.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[20] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
[21] J. Y. Wong. April 27 2016. The Domino Method of Nonlinear Integer/Continuous/Discrete Programming Seeking To
Solve a 19X19 System of Nonlinear Equations, Fourth Edition.
http://myblogsubstance.typepad.com/substance/2016/04/-the-domino-method-of-nonlinear-integercontinuousdiscrete-programming-seeking-to-solve-a-19×19-syste.html.
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