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Primes of the form \({kM^n+n}\)

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Abstract

Erdős and Odlyzko proved that odd integers k such that \({k2^n +1}\) is prime for some positive integer n have a positive lower density. We prove that for sufficiently large x, the number of integers k\({\leq}\)x such that k is relatively prime to M and such that \({kM^n+n}\) is prime for some positive integer n is at least C(M)x for some constant C(M) depending only on M.

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Correspondence to X.-G. Sun.

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Supported by the National Natural Science Foundation of China(11471017) and the National Natural Science Foundation of HuaiHai Institute of Technology (KQ10002).

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Sun, XG. Primes of the form \({kM^n+n}\). Acta Math. Hungar. 158, 100–108 (2019). https://doi.org/10.1007/s10474-019-00914-9

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  • DOI: https://doi.org/10.1007/s10474-019-00914-9

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