Factoring Factorials

Friedlander, Richard J.

doi:10.2307/3027181

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Cited by 2 publications

(2 citation statements)

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“…The prime factorization formula of n! provided in [15] can be summarized as follows: To acquire the prime factorization of n!, we must find, for each of these primes p, the exponent g p of the greatest power of p that divides n!. The formula is connected to the relationship between n, p, and g p .…”

Section: Proofmentioning

confidence: 99%

Mersenne version of Brocard-Ramanujan equation

İBRAHİMOV>

Nalli

2023

Journal of New Results in Science

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In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis. We search for the positive integer solutions of the Brocard-Ramanujan equation for the case where the right-hand side is Mersenne numbers. By using the definition of Mersenne numbers, appropriate inequalities for the parameters of the equation, and the prime factorization of $n!$ we show that there is no positive integer solution to this equation. Thus, we obtain this interesting result demonstrating that the square of any Mersenne number can not be expressed as $n!+1$.

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Section: Proofmentioning

confidence: 99%

Mersenne version of Brocard-Ramanujan equation

İBRAHİMOV>

Nalli

2023

Journal of New Results in Science

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“…In this study, it was shown that there do not exist positive integers m and n that satisfy equation (2). For more versions of Brocard-Ramanujan Diophantine equation, see in [6,8,[10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

A New Version of Brocard-Ramanujan Equation

Ibrahimov,

Emin

2024

Preprint

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Let $(F_{m})_{m\geq0}$ be the Fibonacci sequence defined by $F_{0}=0, F_{1}=1$ and $F_{m+2}=F_{m+1}+F_{m}$ for $m\geq0.$ In this study, we investigate the solution of a Diophantine equations $n!+d=F_{m}$ and in particular $n!+3=F_{m}$ has only the unique positive solution $(n,m)=(2,5)$ which is a special form of the Brocard-Ramanujan equation. MSC Classification: 11D04 , 11D09 , 11D75 , 11B75

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Factoring Factorials

Cited by 2 publications

References 1 publication

Mersenne version of Brocard-Ramanujan equation

Mersenne version of Brocard-Ramanujan equation

A New Version of Brocard-Ramanujan Equation

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