Y by samrocksnature, tastymath75025, FaThEr-SqUiRrEl, icematrix2, megarnie, mathlearner2357, jhu08, Lamboreghini, ImSh95
Let
denote the set of positive integers. Find all functions
such that for positive integers
and
![\[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]](//latex.artofproblemsolving.com/c/1/f/c1f8ffe04cfcc45b498f3931a4796d5c56dc04d0.png)




![\[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]](http://latex.artofproblemsolving.com/c/1/f/c1f8ffe04cfcc45b498f3931a4796d5c56dc04d0.png)
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