Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Received : 2021.08.13
  • Accepted : 2021.12.07
  • Published : 2022.01.30
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Abstract

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.

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Acknowledgement

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

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