Prime periods of periodical P-additive functions - Jakubec, Stanislav (Annales Mathematicae Silesianae, 1998)
I. Korec [Ko] introduced the following definition of a P-additive function. DEFINITION. A function F: N→R is said to be Pythagorean-additive (P-additive, for short) if for all x,y,z∈N x2 = y2+z2 ⇒ F(x) = F(y)+F(z). The aim of this paper is to determine all prime numbers that are periods of P-additive functions. The main result is the following theorem. THEOREM. Let the prime number p be a period of a P-additive function. Then p∈{2,3,5,13}.