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for any m, n in Z there exists a k in Z such that f(k) = f(m) - f(n).

Source: 2015 Saudi Arabia BMO TST II p1

July 24, 2020
algebrafunctional equationfunctionalfunctionIncreasing

Problem Statement

Find all strictly increasing functions f:Z→Rf : Z \to R such that for any m,n∈Zm, n \in Z there exists a k∈Zk \in Z such that f(k)=f(m)−f(n)f(k) = f(m) - f(n).
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