Difference Sets and Polynomials of Prime Variables
نویسندگان
چکیده
Abstract. Let ψ(x) be a polynomial with rational coefficients. Suppose that ψ 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 ∈ A and a prime p such that x− y = ψ(p− 1). Furthermore, if P is a set of primes with the positive relative upper density, then there exist x, y ∈ P and a prime p such that x− y = ψ(p− 1).
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