AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the denominators do not get too large is an ideal expansion. It is shown that Bleicher and Erdös algorithm can be modified to be an ideal algorithm
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
AbstractUniform approximation of functions of a real or a complex variable by a class of linear oper...
AbstractLet x=[d1,···dn,···]E be the Engel continued fraction of x∈[0,1].Call Sn(x)=Σ0≤k<n(x)(dk+1/d...
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...
AbstractA rational number pq is said to be written in Egyptian form if it is presented as a sum of r...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractIt is well-known that the Fibonacci numbers have a maximum property with respect to the leng...
AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 1....
AbstractAn elementary construction of a sequence of positive integers is given. The sequence settles...
AbstractLet A be an infinite sequence of positive integers a1 < a2 <… and put fA(x) = Σa∈A, a≤x(1a),...
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
AbstractUniform approximation of functions of a real or a complex variable by a class of linear oper...
AbstractLet x=[d1,···dn,···]E be the Engel continued fraction of x∈[0,1].Call Sn(x)=Σ0≤k<n(x)(dk+1/d...
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...
AbstractA rational number pq is said to be written in Egyptian form if it is presented as a sum of r...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractIt is well-known that the Fibonacci numbers have a maximum property with respect to the leng...
AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 1....
AbstractAn elementary construction of a sequence of positive integers is given. The sequence settles...
AbstractLet A be an infinite sequence of positive integers a1 < a2 <… and put fA(x) = Σa∈A, a≤x(1a),...
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
AbstractUniform approximation of functions of a real or a complex variable by a class of linear oper...
AbstractLet x=[d1,···dn,···]E be the Engel continued fraction of x∈[0,1].Call Sn(x)=Σ0≤k<n(x)(dk+1/d...
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