Journal of Integer Sequences, Vol. 24 (2021), Article 21.3.7

Nontrivial Effective Lower Bounds for the Least Common Multiple of a q-Arithmetic Progression

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


This paper is devoted to establish nontrivial effective lower bounds for the least common multiple of consecutive terms of a sequence (un)nN whose general term has the form un = r(qn − 1)/(q − 1) + u0, where r, q and u0 are non-negative integers satisfying some specific conditions. This can be considered as a q-analog of the lower bounds already obtained by the author (in 2005) and by Hong and Feng (in 2006) for arithmetic progressions.

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Received September 21 2020; revised version received February 17 2021. Published in Journal of Integer Sequences, February 17 2021.

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