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f(m + f(n)) = f(m) - n

Source: Switzerland - 2019 Swiss MO Final Round p6

December 30, 2022
algebrafunctionalfunctional equation

Problem Statement

Show that there exists no function f:Z→Zf : Z \to Z such that for all m,n∈Zm, n \in Z f(m+f(n))=f(m)−n.f(m + f(n)) = f(m) - n.
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