OBM 2005 Problem 1

A natural number is a palindrome when one obtains the same number when writing its digits in reverse order. For example, $481184$ , $131$ and $2$ are palindromes.

Determine all pairs $(m,n)$ of positive integers such that $\underbrace{111\ldots 1}_{m\ {\rm ones}}\times\underbrace{111\ldots 1}_{n\ {\rm ones}}$ is a palindrome.