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Cool Partitioning Proof Problem

If \( (\sqrt{x^2+1} -x)^{n} = a\sqrt{x^{2}+1}+b\) with \(n \in\mathbb{N}, x \in \mathbb{Z}, x \neq 0, a \in\mathbb{Z}, and \; b \in \mathbb{Z}\).

Prove \( (x^2+1)a^2-b^2 = (-1)^{n+1} \).

Note by Jason Hughes
2 years, 1 month ago

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