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
AbstractIn this paper we obtain the distribution of the functionω(ϕk(n)) which counts the number of ...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
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...
AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all...
AbstractLet z1, …, zn be complex numbers with ∥zj∥1 for j1, …, n. Then maxv=1,…2n |∑j=1n zvj|⩾12√n...
AbstractFor given n, k, the minimum cardinal of any subset B of [1, n] which meets all of the k-term...
AbstractIn this paper we study the distribution modulo 1 of the sequence of vectors (pα1, …, pαk), w...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
AbstractIt is a well-known conjecture that (n2n) is never squarefree if n > 4. It is shown that (n2n...
AbstractFor a > 0 let ψa(x, y) = ΣaΩ(n), the sum taken over all n, 1 ≤ n ≤ x such that if p is prime...
AbstractLetn>2 be an integer, and for each integer 0<a<nwith (a, n)=1, defineāby the congruenceaā≡1 ...
AbstractIn this paper we obtain the distribution of the functionω(ϕk(n)) which counts the number of ...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
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...
AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all...
AbstractLet z1, …, zn be complex numbers with ∥zj∥1 for j1, …, n. Then maxv=1,…2n |∑j=1n zvj|⩾12√n...
AbstractFor given n, k, the minimum cardinal of any subset B of [1, n] which meets all of the k-term...
AbstractIn this paper we study the distribution modulo 1 of the sequence of vectors (pα1, …, pαk), w...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
AbstractWe show that for large N every rational number aN ∈]0, 1[ has an egyptian fraction expansion...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
AbstractIt is a well-known conjecture that (n2n) is never squarefree if n > 4. It is shown that (n2n...
AbstractFor a > 0 let ψa(x, y) = ΣaΩ(n), the sum taken over all n, 1 ≤ n ≤ x such that if p is prime...
AbstractLetn>2 be an integer, and for each integer 0<a<nwith (a, n)=1, defineāby the congruenceaā≡1 ...
AbstractIn this paper we obtain the distribution of the functionω(ϕk(n)) which counts the number of ...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
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