AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion aN = ∑j=1r 1nj where r ≤ (1 + o(1)) log Nlog2N and nr ≤ 4N log2N log2N. This is essentially best possible
In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 1....
AbstractLetαbe a rational fraction with coefficients in a fieldk. The aim of this paper is to invest...
International audienceWe show that, for any fixed $\varepsilon > 0$ and almost all primes $p$, the $...
AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion...
AbstractAn algorithm which yields a short Egyptian fraction expansion in which the denominators stay...
AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the deno...
AbstractA rational number pq is said to be written in Egyptian form if it is presented as a sum of r...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
International audience; Let a a, n, be positive integers that are relatively prime. We say that a/n ...
An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximati...
Given a positive rational number $n/d$ with $d$ odd, its odd greedy expansion starts with the larges...
In this note we prove directly that Golomb’s method and the continued fraction method are essential...
AbstractIn this paper, we establish two mean value theorems for the number of solutions of the Dioph...
AbstractLet {ai} be an increasing sequence of positive integers containing no three distinct element...
Sieve methods have been developed as tools for establishing the existence of prime numbers, or else ...
In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 1....
AbstractLetαbe a rational fraction with coefficients in a fieldk. The aim of this paper is to invest...
International audienceWe show that, for any fixed $\varepsilon > 0$ and almost all primes $p$, the $...
AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion...
AbstractAn algorithm which yields a short Egyptian fraction expansion in which the denominators stay...
AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the deno...
AbstractA rational number pq is said to be written in Egyptian form if it is presented as a sum of r...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
International audience; Let a a, n, be positive integers that are relatively prime. We say that a/n ...
An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximati...
Given a positive rational number $n/d$ with $d$ odd, its odd greedy expansion starts with the larges...
In this note we prove directly that Golomb’s method and the continued fraction method are essential...
AbstractIn this paper, we establish two mean value theorems for the number of solutions of the Dioph...
AbstractLet {ai} be an increasing sequence of positive integers containing no three distinct element...
Sieve methods have been developed as tools for establishing the existence of prime numbers, or else ...
In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 1....
AbstractLetαbe a rational fraction with coefficients in a fieldk. The aim of this paper is to invest...
International audienceWe show that, for any fixed $\varepsilon > 0$ and almost all primes $p$, the $...
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