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Algebra Level 4

Function \(f : \mathbb {R \to R}\) is such that \(f(x+y) = f(x) + f(y) - xy -1\) for all \(x, y \in \mathbb R\) and that \(f(1)=1\).

Find the number of solutions to \(f(n) = n\), where \(n \in \mathbb N\).

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