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