Multiplicative functions additive on polygonal numbers
2021
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.
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