منابع مشابه
Residuacity of Primes
Let q,p be distinct primes with p — ef + 1. A variant of the Kummer-Dedekind theorem is proved for Gaussian periods, which shows in particular that q is an e-th power (modp) if and only if the Gaussian period polynomial of degree e has e (not necessarily distinct) linear factors (modg). This is applied to give a simple criterion in terms of the parameters in the partitions p = 8 / + 1 = X 2 + Y...
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Article history: Received 13 November 2009 Revised 15 March 2011 Accepted 7 June 2011 Available online xxxx Communicated by David Goss MSC: primary 11D09, 11A55 secondary 11R11, 11R29
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A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of th...
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Let pn denote the nth prime. Goldston, Pintz, and Yıldırım recently proved that lim inf n→∞ (pn+1 − pn) log pn = 0. We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let qn denote the nth number that is a product of exactly two distinct primes. We prove that lim inf n→∞ (qn+1 − qn) ≤ 26. If an appropriate generalization of ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1989
ISSN: 0035-7596
DOI: 10.1216/rmj-1989-19-4-1069