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f(x+3/42)+ f(x) = f(x+1/6)+f\left(x+1/7), periodic

Source: Switzerland - Swiss TST 1998 p10

February 19, 2020
periodicfunctionfunctional

Problem Statement

5. Let f:R→Rf : R \to R be a function that satisfies for all x∈Rx \in R (i) ∣f(x)∣≤1| f(x)| \le 1, and (ii) f(x+1342)+f(x)=f(x+16)+f(x+17)f\left(x+\frac{13}{42}\right)+ f(x) = f\left(x+\frac{1}{6}\right)+f\left(x+\frac{1}{7}\right) Prove that ff is a periodic function
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