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- W4300641340 abstract "P. V. Chung showed that there are many multiplicative functions $f$ which satisfy $f(m^2+n^2) = f(m^2)+f(n^2)$ for all positive integers $m$ and $n$. In this article, we show that if more than $2$ squares in the additive condition are involved, then such $f$ is uniquely determined. That is, if a multiplicative function $f$ satisfies [ f(a_1^2 + a_2^2 + dotsb + a_k^2) = f(a_1^2) + f(a_2^2) + dotsb + f(a_k^2) ] for arbitrary positive integers $a_i$, then $f$ is the identity function. In this sense, we call the set of all posotive squares a emph{$k$-additive uniqueness set} for multiplicative functions." @default.
- W4300641340 created "2022-10-03" @default.
- W4300641340 creator A5011909512 @default.
- W4300641340 date "2016-12-02" @default.
- W4300641340 modified "2023-09-30" @default.
- W4300641340 title "$k$-additive uniqueness of the set of squares for multiplicative functions" @default.
- W4300641340 doi "https://doi.org/10.48550/arxiv.1612.00897" @default.
- W4300641340 hasPublicationYear "2016" @default.
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