Arithmetic functions commutable with sums of squares

Abstract

In this note, we characterize all functions $f:\mathbb{N}\to \mathbb{C}$ such that $f(x_1^2+\cdots +x_k^2)=f(x_1{)}^2+\cdots +f(x_k{)}^2$, where $k\ge 3$ and $x_1,\cdots ,x_k$ are positive integers.

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References in corpus (1)

• Multiplicative functions preserving the sum-of-three-squares operation