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I want to find three integers, a b and c, with a^3 + b^3 = 17 * c^3.
all each the smallest integer possible
all each the smallest integer possible
Why not Zurtex? I respect you and Matt's opinions but I'm stubborn. You mind if I check?Zurtex said:Assuming your not looking for the trivial solution (0,0,0) and other trivial solutions like (1, -1, 0). Then mathematica can't find a single instance where it is true.
Actually I just used the FindInstance function for c > 0 and then for c < 0.saltydog said:Alright, I'd like to qualify Zurtx's statement if I may: Mathematica cannot find any value of a and b under 5000 which satisfy the equation. Frankly, if I had access to a faster PC I'd run it up to a million at least as well as optimize my algorithm. It kinds looks like it's related to Fermat's theorem. Is there a proof that there is no solution?
FindInstance? Suppose that's a 5.0 feature. I have 4.1.Zurtex said:Actually I just used the FindInstance function for c > 0 and then for c < 0.
Very well Matt. I'll leave it there.matt grime said:i suspect if you have a basic knowledge of cubic number fields then the answer is known - we can do it for quadratics in quadratic number fields.