On primitive divisors of n^2+b

Graham Everest; Glyn Harman

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On primitive divisors of n^2+b

Graham Everest·Glyn Harman

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Abstract

We study primitive divisors of terms of the sequence P_n=n^2+b, for a fixed integer b which is not a negative square. It seems likely that the number of terms with a primitive divisor has a natural density. This seems to be a difficult problem. We survey some results about divisors of this sequence as well as provide upper and lower growth estimates for the number of terms which have a primitive divisor.

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Graham Everest, Glyn Harman. 2007-01-08. On primitive divisors of n^2+b. https://arxiv.org/abs/math/0701234

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