Bulletin of the Korean Mathematical Society (대한수학회보)

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MULTIPLICATIVE FUNCTIONS COMMUTABLE WITH BINARY QUADRATIC FORMS x2 ± xy + y2

  • Poo-Sung, Park (Department of Mathematics Education Kyungnam University)
  • Received : 2021.12.21
  • Accepted : 2022.04.22
  • Published : 2023.01.31
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Abstract

If a multiplicative function f is commutable with a quadratic form x2 + xy + y2, i.e., f(x2 + xy + y2) = f(x)2 + f(x) f(y) + f(y)2, then f is the identity function. In other hand, if f is commutable with a quadratic form x2 - xy + y2, then f is one of three kinds of functions: the identity function, the constant function, and an indicator function for ℕ ＼ pℕ with a prime p.

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Acknowledgement

This work was supported by Kyungnam University Foundation Grant, 2019.

References

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