Korean J. Math. Vol. 24 No. 1 (2016) pp.107-138
DOI: https://doi.org/10.11568/kjm.2016.24.1.107

Almost-primes represented by $p+a^m$

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Published: Mar 30, 2016
Keywords:
almost-primes, Goldston-Pintz-Y{\i}ld{\i}r{\i}m's method, sieve method
Mathematics Subject Classification:
11P32, 11N36.

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Yaming Lu
School of Mathematics and Statistics Xi’an Jiaotong University Xi’an, Shaanxi, 710049, P. R. China

Abstract

Let $a\geqslant2$ be a fixed integer in this paper. By using the method of Goldston, Pintz and Y{\i}ld{\i}r{\i}m, we will prove that there are infinitely many almost-primes which can be represented as $p+a^m$ in at least two different ways.


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