On the P1 property of sequences of positive integers
Abstract
It is well-known that for any non-constant polynomial P with integer coefficients the sequence (P(n)) n∈ 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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