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Functions and number theory

Source: Brazil Math Olympiad 1995

March 16, 2006
functiongroup theoryabstract algebranumber theorynumber theory proposed

Problem Statement

Find all real-valued functions on the positive integers such that f(x+1019)=f(x)f(x + 1019) = f(x) for all xx, and f(xy)=f(x)f(y)f(xy) = f(x) f(y) for all x,yx,y.
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