Prove that the equation x^2 - y^10 + z^5=6 has no integer* solutions. Try to find a solution!

*integer(negative, positive)

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- Jun 23rd 2013, 10:00 AMtvavladGreat problem!
Prove that the equation x^2 - y^10 + z^5=6 has no integer* solutions. Try to find a solution!

*integer(negative, positive) - Jun 28th 2013, 03:13 PMPhantasmaRe: Great problem!
Let's reduce this to a problem we know how to solve, shall we?

$\displaystyle x^2+z^5-6 = (y^5)^2$ looks suspiciously like the relation from Fermat's Last Theorem. Let's start there.

What would be your next step?

Or, is this just a fun puzzle to challenge people on this forum for ourselves and you don't actually need help?