MathDB
periodic function decomposition

Source: miklos schweitzer 2006 q7

September 3, 2021
periodicalgebrareal analysis

Problem Statement

Suppose that the function f:Z→Zf: Z \to Z can be written in the form f=g1+...+gkf = g_1+...+g_k , where g1,...,gk:Z→Rg_1,. . . , g_k: Z \to R are real-valued periodic functions, with period a1,...,aka_1,...,a_k. Does it follow that f can be written in the form f=h1+..+hkf = h_1 +. . + h_k , where h1,...,hk:Z→Zh_1,. . . , h_k: Z \to Z are periodic functions with integer values, also with period a1,...,aka_1,...,a_k?
Back to ProblemsView on AoPS