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Number theoric function eqution

Source: Iranian third round 2019 Fianls number theory exam problem 1

August 15, 2019
number theory

Problem Statement

Find all functions f:Nā†’Nf:\mathbb{N} \to \mathbb{N} so that for any distinct positive integers x,y,zx,y,z the value of x+y+zx+y+z is a perfect square if and only if f(x)+f(y)+f(z)f(x)+f(y)+f(z) is a perfect square.
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