Question 177
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 $\overbrace{111\ldots1}^{m \text{ones}} \times \overbrace{111\ldots1}^{n \text{ones}}$ is a palindrome.
Determine all pairs $(m, n)$ of positive integers such that $\overbrace{111\ldots1}^{m \text{ones}} \times \overbrace{111\ldots1}^{n \text{ones}}$ is a palindrome.