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Solving Diophantine Equations


Math group,

I am trying to start doing numerical solving of Diophantine Equations. I 
want to do extensive calculations, but the kernel aborts for lack of memory.

For example, the following command aborts midstream:

Table[If[(x^3-1)/(x-1)==(y^n-1)/(y-1) && x!=y,
{{x,y,n},}],{x,2,1000},{y,2,1000},{n,1,1001,2}]

I have tried doing many smaller steps, but then I have a very long file of 
multiple commands.

Would you make a suggestion as to how to process these solving commands with 
large values of the variables?

Thanks,

Diana
-- 
=====================================================
"God made the integers, all else is the work of man."
L. Kronecker, Jahresber. DMV 2, S. 19. 


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