8 citations · 26 across the 41 of their papers we have counts for
Showing 2009 · math.NTShow all
3 papers · 2 filters
math.NT2009
On the series of the reciprocals lcm's of sequences of positive integers: A curious interpretation
Bakir Farhi
In this paper, we prove the following result: {quote} Let $\A$ be an infinite set of positive integers. For all positive integer , let denote the smallest element of $\A$…
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 be an additive basis of order and be a finite nonempty subset of such that the set is still a basis. In this article, we give several upper boun…