# Math Help - Great problem!

1. ## Great problem!

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

2. ## Re: Great problem!

Originally Posted by tvavlad
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?

$x^2+z^5-6 = (y^5)^2$ 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?