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arXiv · 1606.05039

A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$

Lihua You·Yafei Chen·Pingzhi Yuan
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Abstract

In this paper, we mainly discuss the characterization of a class of arithmetic functions $f: N \rightarrow C$ such that $f(u^{2}+kv^2)=f^{2}(u)+kf^{2}(v)$ $(k, u, v \in N)$. We obtain a characterization with given condition, propose a conjecture and show the result holds for $k \in \{2, 3, 4, 5 \}$.

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Lihua You, Yafei Chen, Pingzhi Yuan. 2016-06-16. A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$. https://arxiv.org/abs/1606.05039

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