Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ALMOST-PRIMES REPRESENTED BY p + am

  • Lu, Yaming (School of Mathematics and Statistics Xi'an Jiaotong University)
  • Received : 2015.03.19
  • Accepted : 2016.03.14
  • Published : 2016.03.30
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Abstract

Let $a{\geqslant}2$ be a xed integer in this paper. By using the method of Goldston, Pintz and Yildirm, we will prove that there are innitely many almost-primes which can be represented as $p+a^m$ in at least two dierent ways.

Keywords

Acknowledgement

Supported by : N.S.F.

References

  1. Y. G. Chen and X. G. Sun, On Romanoff's constant, J. Number Theory 106 (2004), 275-284. https://doi.org/10.1016/j.jnt.2003.11.009
  2. P. Erdos, On integers of the form $2^k$ + p and some related problems, Summa Brasil. Math. 2 (1950), 113-123.
  3. J. B. Friedlander and H. Iwaniec, Hyperbolic prime number theorem, Acta Math. 202 (2009), 1-19. https://doi.org/10.1007/s11511-009-0033-z
  4. J. B. Friedlander and H. Iwaniec, Opera de Cribro, Colloquium Publications (vol.57), American Mathematical Society, Providence, Rhode Island, 2010.
  5. D. A. Goldston, J. Pintz, and C. Y. Yildirim, Primes in tuples I, Ann. of Math. 170 (2009), 819-862. https://doi.org/10.4007/annals.2009.170.819
  6. L. Habsieger, X. Roblot, On integers of the form p+$2^k$, Acta Arith. 122 (2006), 45-50. https://doi.org/10.4064/aa122-1-4
  7. J. Pintz, A note on Romanoff's constant, Acta Math. Hungar. 112 (2006), 1-14. https://doi.org/10.1007/s10474-006-0060-6
  8. K. Prachar, Uber einen Satz der additiven Zahlentheorie, Monatsh. Math. 56 (1952), 101-104. https://doi.org/10.1007/BF01412828
  9. N. P. Romanoff, Uber einige Satze der additiven Zahlentheorie, Math. Ann. 109 (1934), 668-678. https://doi.org/10.1007/BF01449161
  10. K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc. 44 (2007), 1-18.