Difference sets and Polynomials of prime variables
Number Theory
2007-11-08 v3 Combinatorics
Abstract
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).
Cite
@article{arxiv.0709.1758,
title = {Difference sets and Polynomials of prime variables},
author = {Hongze Li and Hao Pan},
journal= {arXiv preprint arXiv:0709.1758},
year = {2007}
}