Nontrivial Lower Bounds for the p-adic Valuation of Certain Rational Numbers
Laboratoire de Mathématiques Appliquées
Faculté des Sciences Exactes
Université de 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.
Full version: pdf,
(Concerned with sequences
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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