Prime numbers p with expression p = a2 ± ab ± b2

JOURNAL OF NUMBER THEORY

卷:166

Article

Bahmanpour, Kamal¹ 

[1] Univ Mohaghegh Ardabili, Fac Math Sci, Dept Math, Ardebil 5619911367, Iran

关键词: Binary quadratic form;    Finite group;    Law of quadratic reciprocity;    Prime number;    Semi-group;   

DOI  :  10.1016/j.jnt.2016.02.024

来源: Elsevier

【 摘 要 】

Let p be a prime number. In this paper we show that p can be expressed as p = a(2) +/- ab - b(2) with integers a and b if and only if p is congruent to 0, 1 or -1 (mod 5) and p can be expressed as p = a(2) +/- ab +/- b(2) with integers a and b if and only if p is congruent to 0, 1 (mod 3). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free