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functional in Z, f(f(x)) = x, if x + y is odd then f(x) + f(y) \ge x + y

Source: Dutch IMO TST3 2019 p3

January 11, 2020
Functional inequalityFind all functionsalgebra

Problem Statement

Find all functions f:Z→Zf : Z \to Z satisfying the following two conditions: (i) for all integers xx we have f(f(x))=xf(f(x)) = x, (ii) for all integers xx and y such that x+yx + y is odd, we have f(x)+f(y)≥x+yf(x) + f(y) \ge x + y.
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