Determine all possible pairs (x,y) of positive integers such that:
x+1 y+1
Each of ---- and ----- is a positive integer.
y x
**** Adapted from a problem appearing in Polish Mathematical Olympiad.
(In reply to
re: Analytical solution by Jer)
The very first step is legitimate. If each of them individually is an integer, then their product must necessarily be an integer. However, you are correct that this is not sufficient. My approach finds all possible "solutions", but it might also find a few non-solutions. As a last step, I need to check that each of the "solutions" satisfy the initial condition. It turns out that they all do.
re(2): Analytical solution
