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Find n with 2021 solutions to x^2-y^2=n

Source: Spain Mathematical Olympiad 2021 P2

May 10, 2021
Spainnumber theorynumber of divisors

Problem Statement

Given a positive integer nn, we define λ(n)\lambda (n) as the number of positive integer solutions of x2−y2=nx^2-y^2=n. We say that nn is olympic if λ(n)=2021\lambda (n) = 2021. Which is the smallest olympic positive integer? Which is the smallest olympic positive odd integer?
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