Difference sets and Polynomials of prime variables

Details Difference sets and Polynomials of prime variables Difference sets and Polynomials of prime variables

2007-09-12

arxiv.org/abs/0709.1758v3

Mathematics

Number Theory

Scientific paper

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).

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