국가지식-학술정보
MERSENNE PRIME FACTOR AND SUM OF BINOMIAL COEFFICIENTS
- 한국전산응용수학회
- Journal of applied mathematics & informatics
- Vol.40 No.1
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2022.0161 - 68 (8 pages)
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DOI : 10.14317/jami.2022.061
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Let M<sub>p</sub> := 2<sup>p</sup> - 1 be a Mersenne prime. In this article, we find integers a, b, c, d, e and n satisfying <TEX>$sum_{t=0}^{n};({an+b\ct+d});=;M_{p^e}$</TEX> given a Mersenne prime number M<sub>p</sub>. 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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