Sid Ali Bousla

most citedNontrivial effective lower bounds for the least common multiple of some quadratic sequences

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math.NT2020

Effective estimates for the least common multiple of some integer sequences

Sid Ali Bousla

This thesis is devoted to studying estimates of the least common multiple of some integer sequences. Our study focuses on effective bounding of the $lcm$ of some class of…

math.NT2020

On the least common multiple of binary linear recurrence sequences

Sid Ali Bousla

In this paper, we present a method for estimating the least common multiple of a large class of binary linear recurrence sequences. Let $P, Q, R_{0}$ , and $R_{1}$ be fixed integers and l…

math.NT2020

Nontrivial upper bounds for the least common multiple of an arithmetic progression

Sid Ali Bousla

In this paper, we establish some nontrivial and effective upper bounds for the least common multiple of consecutive terms of a finite arithmetic progression. Precisely, we prove th…

math.NT2020★ 1 cited

Nontrivial effective lower bounds for the least common multiple of some quadratic sequences

Sid Ali Bousla, Bakir Farhi

This paper is devoted to studying the numbers $L_{c, m, n} := lcm {m^{2} + c, (m + 1)^{2} + c, \dots, n^{2} + c}$ , where $c, m, n$ are positive integers such that $m \leq n$ . Precisely,…

math.NT2019

Identities and estimations involving the least common multiple of strong divisibility sequences

Sid Ali Bousla, Bakir Farhi

In this paper, we first prove that for any strong divisibility sequences $a = (a_{n})_{n \geq 1}$ , we have the identity: $\mathrm{lcm} \left\lbrace \binom{n}{0…