**Problem:** Solve the equation for positive integers x, y.

**Discussion:**

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.

## Chatuspathi:

**Paper:**RMO 2015 (Chennai)**What is this topic:**Number Theory**What are some of the associated concepts:**Diophantine Equation**Where can learn these topics:**Cheenta**Book Suggestions:**Theory of Numbers by Sierpinsky