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}.
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Vol. 12 (1998)
Published: 1998-09-30
10.1515/amsil
English