Cubic and quartic congruences modulo a prime

被引：17

作者：

Sun, ZH ^{[1
]}

机构：

[1] Huaiyin Teachers Coll, Dept Math, Huainan 223001, Jiangsu, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2003年 / 102卷 / 01期

关键词：

cubic congruence; quartic congruence; recurring sequence;

D O I：

10.1016/S0022-314X(03)00067-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p > 3 be a prime, and N-p(f (x)) denote the number of solutions of the congruence f (x) equivalent to 0 (mod p). In this paper, using the third-order recurring sequences we determine the values of N-p(x(3) +a(1)x(2) + a(2)x + a(3)) and N-p (x(4) + ax(2) + bx + c), and construct the solutions of the corresponding congruences, where a(1), a(2), a(3) a, b, c are integers. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：41 / 89

页数：49

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