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All functions with f(m^2+3n^2)=(f(m))^2 + 3(f(n))^2

Source: Vietnam Northern Summer Camp of Mathematics, 2011 - P2

August 15, 2011

functionnumber theory proposednumber theory

Problem Statement

Find all functions

f: \mathbb N \cup \{0\} \to \mathbb N\cup \{0\}

such that

f(1)>0

and f(m^2+3n^2)=(f(m))^2 + 3(f(n))^2 \forall m,n \in \mathbb N\cup \{0\}.