Bakir Farhi

most citedAn identity involving the least common multiple of binomial coefficients and its application

2 citations · 2 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2009★ 2 cited

An identity involving the least common multiple of binomial coefficients and its application

Bakir Farhi

In this paper, we prove the identity $$\lcm\{\binom{k}{0}, \binom{k}{1}, >..., \binom{k}{k}\} = \frac{\lcm(1, 2, ..., k, k + 1)}{k + 1} (\forall k \in \mathbb{N}) .$$ As an applica…

math.NT2009

Upper bounds for the order of an additive basis obtained by removing a finite subset of a given basis

Bakir Farhi

Let $A$ be an additive basis of order $h$ and $X$ be a finite nonempty subset of $A$ such that the set $A ∖ X$ is still a basis. In this article, we give several upper boun…

math.NT2006

About the fractional parts of the powers of the rational numbers

Bakir Farhi

Let $p / q$ ( $p, q \in N^{*}$ ) be a positive rational number such that $p > q^{2}$ . We show that for any $ε > 0$ , there exists a set $A (ε) \subset [0, 1 [$ , with finite border and…