Difference Sets and the Primes
نویسندگان
چکیده
Suppose that A ⊂ {1, . . . , N} is such that the difference between any two elements of A is never one less than a prime. We show that |A| = O(N exp(−c 4 √ logN)) for some absolute c > 0.
منابع مشابه
On the Associated Primes of the generalized $d$-Local Cohomology Modules
The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary generalized local cohomology modules. Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$ are finitely generated $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...
متن کاملاختلال در شبکه معنایی بیماران اسکیزوفرنیک: آمادهسازی معنایی با ارائه همزمان دو آمادهساز
Abstract Objectives: The present study was designed to investigate the automatic activation of seman-tic priming in schizophrenic patients. Method: 36 schizophrenic patients and 36 normal sub-jects participated in two experiments. In experiment one, the effect of semantic relation on iden- tification of degraded targets was examined between a series of single prime words and single target words...
متن کاملSquares and Difference Sets in Finite Fields
For infinitely many primes p = 4k+1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Zp such that the difference set B−B contains only quadratic residues. Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B| ≤ √ p − 1, under suitable conditions on p. The new bound is valid for approximately three quarters of the primes p = 4k + 1.
متن کاملA trace representation of binary Jacobi sequences
We determine the trace function representation, or equivalently, the Fourier spectral sequences of binary Jacobi sequences of period pq, where p and q are two distinct odd primes. This includes the twin-prime sequences of period p(p + 2) whenever both p and p + 2 are primes, corresponding to cyclic Hadamard difference sets. c © 2008 Elsevier B.V. All rights reserved.
متن کاملThe power digraphs of safe primes
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...
متن کامل