On the $P_1$ property of sequences of positive integers

Tigran Hakobyan

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arXiv · 1601.04886

On the $P_1$ property of sequences of positive integers

Tigran Hakobyan

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Abstract

It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P(n))_{ n\in \mathbb N}$ has the property that there are infinitely many prime numbers dividing at least one term of this sequence. Certainly, there is a proof based on the Chinese Remainder Theorem. In this paper we give proofs of two analytic criteria revealing this property of sequences.

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Tigran Hakobyan. 2016-01-19. On the $P_1$ property of sequences of positive integers. https://arxiv.org/abs/1601.04886

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