Problem

Source: Spain Mathematical Olympiad 2021 P2

Tags: Spain, number theory, number of divisors



Given a positive integer $n$, we define $\lambda (n)$ as the number of positive integer solutions of $x^2-y^2=n$. We say that $n$ is olympic if $\lambda (n) = 2021$. Which is the smallest olympic positive integer? Which is the smallest olympic positive odd integer?