Try this problem from RMO 2015 from Chennai Region based on Integer Solution of Polynomial.
Problem: Integer Solution of Polynomial
Solve the equation for positive integers x, y.
Adding 1 to both sides and adjusting we get
We have two cases :
Case 1: implying
This is an easy check (plug in 1, 2, ... , 10).
We find works.
Case 2: implying
Then y is at least x+1.
But this implies
But x is a positive integer. Hence this is not possible.