AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over all expansions of aN, and let D(N) = max{D(a,N): 1 ≤ a < N}. Then D(N)N ≤ (logN)32+ϵ, where ϵ →0 as N → ∞, improving the result of M.N. Bleicher and P. Erdös
AbstractWe show that [formula]. Here pn and qn are the numerators and denominators of the convergent...
Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception,...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
AbstractAn algorithm which yields a short Egyptian fraction expansion in which the denominators stay...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion...
Let a, n be positive integers that are relatively prime. We say that a/n can be represented as an Eg...
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...
We prove upper and lower bound for the average value over primes p of the number of positive integer...
International audience; Let a a, n, be positive integers that are relatively prime. We say that a/n ...
An Egyptian fraction is the sum of unit fractions , usually distinct. For example, the Egyptian frac...
An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximati...
AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all...
AbstractWe show that [formula]. Here pn and qn are the numerators and denominators of the convergent...
Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception,...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
AbstractAn algorithm which yields a short Egyptian fraction expansion in which the denominators stay...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion...
Let a, n be positive integers that are relatively prime. We say that a/n can be represented as an Eg...
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...
We prove upper and lower bound for the average value over primes p of the number of positive integer...
International audience; Let a a, n, be positive integers that are relatively prime. We say that a/n ...
An Egyptian fraction is the sum of unit fractions , usually distinct. For example, the Egyptian frac...
An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximati...
AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all...
AbstractWe show that [formula]. Here pn and qn are the numerators and denominators of the convergent...
Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception,...
AbstractLet A*k(n) be the number of positive integers a coprime to n such that the equation a/n=1/m1...
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