NL-NWO 2009 Problem 1

In this problem, we consider integers consisting of $5$ digits, of which the rst and last one are nonzero. We say that such an integer is a palindromic product if it satises the following two conditions:

• the integer is a palindrome, (i.e. it doesn't matter if you read it from left to right, or the other way around);
• the integer is a product of two positive integers, of which the first, when read from left to right, is equal to the second, when read from right to left, like $4831$ and $1384$ . For example, $20502$ is a palindromic product, since $102 \cdot 201 = 20502$ , and $20502$ itself is a palindrome. Determine all palindromic products of $5$ digits.