Multiplicative functions additive on generalized pentagonal numbers

作者：Kim Byungchan^*; Kim Ji Young; Lee Chong Gyu; Park Poo Sung

来源：Comptes Rendus Mathematique, 2018, 356(2): 125-128.

DOI：10.1016/j.crma.2017.12.011

We prove that the set GP of all nonzero generalized pentagonal numbers is an additive uniqueness set; if a multiplicative function f satisfies the equation
f (a + b) = f (a) + f (b),
for all a, b is an element of GP, then f is the identity function.

• 出版日期2018-2