AbstractLet D(a, N) = min{nk: aN = Σ1k 1ni, n1 < n2 < … < nk, ni ∈ Z}, where minimum ranges over all expansions of aN, and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(MN) ≤ max{MD(N), ND(M)} ≤ D(M) D(N), establishing a conjecture made by M. N. Bleicher and P. Erdös
AbstractLet z1, …, zn be complex numbers with ∥zj∥1 for j1, …, n. Then maxv=1,…2n |∑j=1n zvj|⩾12√n...
AbstractAs an extension of the Dirichlet divisor problem, S. Chowla and H. Walum conjectured that, a...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
AbstractIt is shown that if AϵΩn−{Jn} satisfies nkσk(A)⩾(n−k+1)2 σk−1(A) (k=1,2,…,n), where σk(A) de...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
AbstractAs to the conjecture that given m ϵ N = {1,2,3,…}, the sequence {mn}n⩾0, defined by the iter...
AbstractIt is a well-known conjecture that (n2n) is never squarefree if n > 4. It is shown that (n2n...
AbstractLetB(m) denote the number of ones in the binary expansion of an integerm⩾2. We prove that li...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the deno...
AbstractLet x1 < x2 … < xb be integers ≥ 1 such that gcd(x1, …, xb) = 1. Let S be the additive subse...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
AbstractLet z1, …, zn be complex numbers with ∥zj∥1 for j1, …, n. Then maxv=1,…2n |∑j=1n zvj|⩾12√n...
AbstractAs an extension of the Dirichlet divisor problem, S. Chowla and H. Walum conjectured that, a...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractLet D(a,N) = min{nk:aN = Σ1k1ni, n1 < n2 < … < nk, ni ϵ Z0}, where the minimum ranges over a...
AbstractIt is shown that if AϵΩn−{Jn} satisfies nkσk(A)⩾(n−k+1)2 σk−1(A) (k=1,2,…,n), where σk(A) de...
AbstractLet D(a, N) = min{nk:aK = ∑1k 1n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
AbstractAs to the conjecture that given m ϵ N = {1,2,3,…}, the sequence {mn}n⩾0, defined by the iter...
AbstractIt is a well-known conjecture that (n2n) is never squarefree if n > 4. It is shown that (n2n...
AbstractLetB(m) denote the number of ones in the binary expansion of an integerm⩾2. We prove that li...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
AbstractIf b(m;n) denotes the number of partitions of n into powers of m, then b(m; mr+1n) ≡ b(m; mr...
AbstractWe say that an algorithm which could yield a short unit fraction expansion in which the deno...
AbstractLet x1 < x2 … < xb be integers ≥ 1 such that gcd(x1, …, xb) = 1. Let S be the additive subse...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
AbstractLet z1, …, zn be complex numbers with ∥zj∥1 for j1, …, n. Then maxv=1,…2n |∑j=1n zvj|⩾12√n...
AbstractAs an extension of the Dirichlet divisor problem, S. Chowla and H. Walum conjectured that, a...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
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