DOI QR코드

DOI QR Code

MERSENNE PRIME FACTOR AND SUM OF BINOMIAL COEFFICIENTS

  • JO, GYE HWAN (Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University) ;
  • KIM, DAEYEOUL (Department of Mathematics and Institute of Pure and Applied Mathematics, Jeonbuk National University)
  • 투고 : 2021.08.13
  • 심사 : 2021.12.07
  • 발행 : 2022.01.30

초록

Let Mp := 2p - 1 be a Mersenne prime. In this article, we find integers a, b, c, d, e and n satisfying $\sum_{t=0}^{n}\;\({an+b\\ct+d}\)\;=\;M_{p^e}$ given a Mersenne prime number Mp. In order to find a special case that satisfies the above results, we reprove an well-known relation of a certain sum of binomial coefficients and a divisor function.

키워드

과제정보

This work is supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1F1A1051093).

참고문헌

  1. L.E. Dickson, History of the theory of numbers. Vol. I: Divisibility and primality, Cresse Chelsea Publishing Co., New York, 1966.
  2. R.K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, New York, 2004.
  3. I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, Academic press, 2014.
  4. D. Kim and A. Bayad, Polygon Numbers Associated with the Sum of Odd Divisors Function, Exp. Math. 26 (2017), 287-297. https://doi.org/10.1080/10586458.2016.1162231
  5. D. Kim and A. Bayad, S. Park, Iterated stable numbers and iterated amicable pairs, To appear in Math. Meth. Appl Sci. doi.org/10.1002/mma.7555.
  6. J.H. Silverman, A friendly introduction to number theory, Pearson, 2012.
  7. K.S. Williams, Number theory in the spirit of Liouville. Vol. 76. Cambridge University Press, 2011.