Can anyone give the value for x,c,d (x,c,d are all integer and >1) for which 3.x(x+c).c+c^3 =d^3?

Question

Can any one give an example where 3.x.c(x+c)+c^3 will be a cube of an integer>1. The value of x and c are >0 and and x,c are integer

Answer 1

3xc(x+c) + c^3 =d^3
3cx^2 + 3c^2x + c^3 = d^3
x^3 + 3cx^2 + 3(c^2)x + c^3 = d^3 + x^3
(x + c )^3 = d^3 + x^3
This equation has no positive integer solution by Fermat's last
theorem.
No one can give an example!

Answer 2

Cubic Diophantine equations aren't real fun to play with analytically.

I'd suggest setting up a quick computer program with nested loops in x and c and just 'brute force' the problem for x and c values up to a thousand or so and see what you get.


Doug

Answer 3

I think you should do your own maths homework

Answer 4

Its a trial & error method. Is there a solution? I don't think. If so, please publish.