Mathematics > Number Theory
[Submitted on 12 Sep 2007 (v1), last revised 8 Nov 2007 (this version, v3)]
Title:Difference sets and Polynomials of prime variables
View PDFAbstract: Let \psi(x) be a polynomial with rational coefficients. Suppose that \psi has the positive leading coefficient and zero constant term. Let A be a set of positive integers with the positive upper density. Then there exist x,y\in A and a prime p such that x-y=\psi(p-1). Furthermore, if P be a set of primes with the positive relative upper density, then there exist x,y\in P and a prime p such that x-y=\psi(p-1).
Submission history
From: Hao Pan [view email][v1] Wed, 12 Sep 2007 12:00:12 UTC (13 KB)
[v2] Fri, 26 Oct 2007 02:53:01 UTC (14 KB)
[v3] Thu, 8 Nov 2007 12:25:08 UTC (19 KB)
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