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Suppose that \(a, b \in \mathbb{N}\) and that \(a^2 - b^2\) is a prime number. What relation exists between \(a\) and \(b\)?
Show that \(401\) is a prime number, then solve the following equation in \(\mathbb{N}^2\): $$x^2 - y^2 = 401$$
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