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Miklós Schweitzer 1985, Problem 7

Source: Miklós Schweitzer 1985

September 5, 2016
Miklos Schweitzercollege contestsfunctionreal analysis

Problem Statement

Let p1p_1 and p2p_2 be positive real numbers. Prove that there exist functions fi ⁣:R→Rf_i\colon \mathbb R \rightarrow \mathbb R such that the smallest positive period of fif_i is pi (i=1,2)p_i\, (i=1, 2), and f1−f2f_1-f_2 is also periodic. [J. Riman]
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