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MathNet 2015-part-06 — 191 problems (EN–VI) Question 95

Math Olympiad Vault · MathNet 2015-part-06 — 191 problems (EN–VI)

Question 95

Find all maps $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that $f(n)+f(n+1)=2 n+1$ for every integer $n$ and moreover

$$
\sum_{i=1}^{63} f(i)=2015
$$