An integer $d$ is called a factor of an integer $n$ if there is an integer $q$ such that $n = qd$. In particular the set of factors of $n$ contains $n$ and contains 1. You are given that $2024 = 8 \times 11 \times 23$.
Write the number of ordered pairs $(a,b)$ of positive integers such that $a^2 - b^2 = 2024^2$. If there are infinitely many such pairs, write the word infinite as your answer. [3 points]