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Israel 2016 Q7 - functional equation Z->C

Source: Israel National Olympiad 2016 Q7

August 7, 2019
algebrafunctional equationfunction

Problem Statement

Find all functions f:Zā†’Cf:\mathbb{Z}\rightarrow\mathbb{C} such that f(x(2y+1))=f(x(y+1))+f(x)f(y)f(x(2y+1))=f(x(y+1))+f(x)f(y) holds for any two integers x,yx,y.
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