Journal of Integer Sequences, Vol. 26 (2023), Article 23.6.1

Nontrivial Lower Bounds for the p-adic Valuation of Certain Rational Numbers

Bakir Farhi
Laboratoire de Mathématiques Appliquées
Faculté des Sciences Exactes
Université de Bejaia
06000 Bejaia


We show that the p-adic valuation (where p is a given prime number) of certain rational numbers is unusually large. This generalizes very recent results of the author and of Dubickas, which are both related to the special case p = 2. The crucial point for obtaining our main result is the fact that the p-adic valuation of the rational numbers in question is unbounded from above. We confirm this fact by three different methods; the first two are elementary, while the third one relies on p-adic analysis.

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(Concerned with sequences A002944 A087910.)

Received March 11 2023; revised versions received March 16 2023; June 11 2023. Published in Journal of Integer Sequences, June 12 2023.

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