Journal of Integer Sequences, Vol. 23 (2020), Article 20.6.6

Nontrivial Effective Lower Bounds for the Least Common Multiple of Some Quadratic Sequences


Sid Ali Bousla and Bakir Farhi
Laboratoire de Mathématiques appliquées
Faculté des Sciences Exactes
Université de Bejaia
06000 Bejaia
Algeria

Abstract:

This paper is devoted to studying the numbers

Lc,m,n := lcm (m2 + c, (m+1)2 + c, ..., n2 + c),

where c, m, n are positive integers such that m ≤ n. More precisely, we determine a nontrivial rational divisor of Lc,m,n and then we derive (as consequences) some non-trivial lower bounds for Lc,m,n . Our approach (focusing on commutative algebra) is new and different from those using previously by Farhi, Oon, and Hong.

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Received January 30 2020; revised versions received May 8 2020; May 14 2020. Published in Journal of Integer Sequences, June 22 2020.

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