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We prove that the set $$\mathcal {P}$$ ( $$\mathcal {H}$$ , resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions;… Click to show full abstract
We prove that the set $$\mathcal {P}$$ ( $$\mathcal {H}$$ , resp.) of all positive pentagonal (hexagonal, resp.) numbers is an additive uniqueness set for the collection of multiplicative functions; if a multiplicative function f satisfies the equation $$\begin{aligned} f(a+b) = f(a) + f(b) \end{aligned}$$ for all $$a, b \in \mathcal {P}$$ ( $$\mathcal {H}$$ , resp.), then f is the identity function.
Keywords:
polygonal numbers;
additive polygonal;
resp;
multiplicative functions;
functions additive
Journal Title: Aequationes mathematicae
Year Published: 2021
Link to full text (if available)
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Journal Title: Aequationes mathematicae
Year Published: 2021
Link to full text (if available)
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recommendations!