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Almost-primes represented by $p+a^m$
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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.
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.
참고문헌 (10)
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- J. B. Friedlander, "Hyperbolic prime number theorem", Acta Math, 202, pp.1~19 (2009)
- J. B. Friedlander, "Opera de Cribro" (2010), American Mathematical Society
- D. A. Goldston, "Primes in tuples I", Ann. of Math, 170, pp.819~862 (2009)
- L. Habsieger, "On integers of the form p+2k", Acta Arith, 122, pp.45~50 (2006)
- J. Pintz, "A note on Romanoff's constant", Acta Math. Hungar, 112, pp.1~14 (2006)
- K. Prachar, "Uber einen Satz der additiven Zahlentheorie", Monatsh. Math, 56, pp.101~104 (1952)
- N. P. Romanoff, "Uber einige Satze der additiven Zahlentheorie", Math. Ann, 109, pp.668~678 (1934)
- K. Soundararajan, "Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim", Bull. Amer. Math. Soc, 44, pp.1~18 (2007)
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