492 citations
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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.NT2015
On the possible quantities of Fibonacci numbers that occur in some type of intervals
Bakir Farhi
In this paper, we show that for any integer , each of the intervals () contains either $\left\lfloor \frac{\log a}{\logΦ}\right\rflo…
math.NT2013★ 1 cited
A curious formula related to the Euler Gamma function
Bakir Farhi
In this note, we prove that for all , we have: $$ \logΓ(x) = \frac{1}{2} \logπ+ π\boldsymbolη \left(\frac{1}{2} - x\right) - \frac{1}{2} \log\sin(πx) + \frac{1}π \su…
math.NT2010
Algebraic and topological structures on the set of mean functions and generalization of the AGM mean
Bakir Farhi
In this paper, we present new structures and results on the set $\M_\D$ of mean functions on a given symmetric domain $\D$ of . First, we construct on $\M_\D$ a struc…