# New friendship!

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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