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arXiv · 1903.10166

Multiplicative functions which are additive on sums of two nonzero squares

Poo-Sung Park
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Abstract

Let $f$ be a multiplicative function which satisfies \[ f(a^2+b^2+c^2+d^2) = f(a^2+b^2)+f(c^2+d^2) \] for positive integers $a$, $b$, $c$, and $d$. We show that $f$ is the identity function provided that $f(3)\,f(11) \ne 0$. Otherwise, $f(n)=0$ for all $n \ge 2$ except for $n=3,9,11$.

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Poo-Sung Park. 2019-03-25. Multiplicative functions which are additive on sums of two nonzero squares. https://arxiv.org/abs/1903.10166

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