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Periodic functions s.t. f(x^2y) = (f(x))^2f(y)

Source: 2002 Austrian-Polish, problem 7

September 23, 2006
functionalgebra unsolvedalgebrafunctional equation

Problem Statement

Find all real functions ff definited on positive integers and satisying:
(a) f(x+22)=f(x)f(x+22)=f(x),
(b) f(x2y)=(f(x))2f(y)f\left(x^{2}y\right)=\left(f(x)\right)^{2}f(y)
for all positive integers xx and yy.
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