Determine all positive integer solutions of x2y
Of course, for y>1 you could use Fermat's theorem, but that would be unsporting!
(In reply to All solutions
by Old Original Oskar!)
Oskar's solution is correct, but I think he has a typo; the only solution to the problem should be x=3, y=1.
(I also cheated and used Fermat's Last Theorem!)