Difference between revisions of "2021 USAJMO Problems/Problem 1"
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==Problem== | ==Problem== | ||
− | + | Let <math>\mathbb{N}</math> denote the set of positive integers. Find all functions <math>f : \mathbb{N} \rightarrow \mathbb{N}</math> such that for positive integers <math>a</math> and <math>b,</math><cmath>f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.</cmath> | |
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==Solution== | ==Solution== |
Revision as of 14:32, 15 April 2021
Problem
Let denote the set of positive integers. Find all functions
such that for positive integers
and