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f(f(n))=n=f(f(n+2)+2) (I Soros Olympiad 1994-95 Ukraine R2 10.1)

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June 6, 2024
algebranumber theoryfunctional

Problem Statement

The function f:Z→Zf: Z \to Z satisfies the following conditions: 1) f(f(n))=nf(f(n))=n for all integers nn 2) f(f(n+2)+2)=nf(f(n+2)+2) = n for all integers nn 3) f(0)=1f(0)=1. Find the value of f(1995)f(1995) and f(−1994)f(-1994).
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