Multiplicative on Squares

★ 7/10functions number theory sequences Induction Casework Functional Equations

Problem

A sequence $\{a_n\}$ of positive integers satisfies, for all positive integers $m, k$ ,

a_{m^2} = a_m^2, \qquad a_{m^2 + k^2} = a_m a_k.

Find a closed formula for $a_n$ .

Answer

Solution

Difficulty	7/10
Topics	functions, number theory, sequences, Induction, Casework, Functional Equations

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