On a class of prime-detecting congruences

被引：1

作者：

Shonhiwa, T ^{[1
]}

机构：

[1] Chowan Coll, Dept Math, Murfreesboro, NC 27855 USA

来源：

DISCRETE MATHEMATICS | 1999年 / 204卷 / 1-3期

关键词：

D O I：

10.1016/S0012-365X(98)00380-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Gould (The Fibonacci Quarterly 2 (1964) 241-260) proved the general inversion theorem: for any ordered sequence pair [f(n, k), g(n, k)] [GRAPHICS] where R(n, k) is the number of compositions of n greater than or equal to 1 into k relatively prime parts and [GRAPHICS] is its inverse. In this paper, we obtain a variety of such ordered inversion pairs. Further, we give necessary and sufficient conditions for the congruence f(n, k) = g(n, k) (mod k) to hold, in particular criteria for k greater than or equal to 2 to be a prime when the congruence holds for all n greater than or equal to 1. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：357 / 368

页数：12