Mersenne version of brocard-ramanujan equation
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Tarih
2023
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 $n!+1$.
Açıklama
Anahtar Kelimeler
Kaynak
Journal of New Results in Science
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Cilt
12
Sayı
1
