On finiteness of odd superperfect numbers

Tomohiro Yamada

doi:10.5802/jtnb.1121

Tomohiro Yamada

Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 1, pp. 259-274.

Résumé
Abstract

On montre de nouveaux résultats sur l’équation $σ (N) = a M$ , $σ (M) = b N .$ On en déduit, comme corollaire, qu’il n’existe qu’un nombre fini de nombres impairs superparfaits ayant un nombre fixé de facteurs premiers distincts.

Some new results concerning the equation $σ (N) = a M$ , $σ (M) = b N$ are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.

Reçu le : 2019-06-28
Révisé le : 2020-02-06
Accepté le : 2020-02-21
Publié le : 2020-08-21

DOI : https://doi.org/10.5802/jtnb.1121
Classification : 11A25, 11A05, 11D61, 11J86
Mots clés : Odd perfect numbers, multiperfect numbers, superperfect number; the sum of divisors, arithmetic functions, exponential diophantine equations.

@article{JTNB_2020__32_1_259_0,
     author = {Tomohiro Yamada},
     title = {On finiteness of odd superperfect numbers},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {259--274},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {32},
     number = {1},
     year = {2020},
     doi = {10.5802/jtnb.1121},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1121/}
}

Tomohiro Yamada. On finiteness of odd superperfect numbers. Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 1, pp. 259-274. doi : 10.5802/jtnb.1121. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1121/

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