# 2008 JBMO Problems/Problem 3

## Problem

Find all prime numbers , such that

## Solution

The given equation can be rearranged into the below form:

then we have

and and

then we have

and and

note that if , then which is a contradiction.

and

then we have

and and We have that exactly one of is a multiple of .

cannot be a multiple of since . Since is prime, then we have is a prime.
contradiction.

Also, cannot be a multiple of since, contradiction.

So,
and

Thus we have the following solutions: