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The primes contain arbitrarily long polynomial progressions

Acta Mathematica, no. 2 (2008): 213-305

Cited: 125|Views27

Abstract

We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P 1, …, P k  ∈ Z[m] in one unknown m with P 1(0) = … = P k (0) = 0, and given any ε > 0, we show that there are infinitely many integers x and m, with , such that x + P 1(m), …, x + P k (...More

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