On a class of arithmetical sets
On a class of combinatorial Diophantine equations.
On a class of combinatorial sums involving generalized factorials.
On a class of densities of sets of positive integers.
On a class of polynomials with integer coefficients.
On a class of ternary inclusion-exclusion polynomials.
On a class of Thue-Morse type sequences.
On a combinatorial problem of Asmus Schmidt.
On a congruence of Emma Lehmer related to Euler numbers
A congruence of Emma Lehmer (1938) for Euler numbers modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which play an important role, and we present some numerical results.
On a conjecture concerning sequences of the third order
On a conjecture of Erdös and Heilbronn
On a conjecture of Hamidoune for subsequence sums.
On a conjecture of Lemke and Kleitman
On a conjecture of Morgan Ward, I
On a conjecture of Morgan Ward, II
On a conjecture of Morgan Ward, III
On a conjecture of Sárközy and Szemerédi
Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. In 1994, Sárközy and Szemerédi conjectured that there exist infinite additive complements A and B with lim sup A(x)B(x)/x ≤ 1 and A(x)B(x)-x = O(minA(x),B(x)), where A(x) and B(x) are the counting functions of A and B, respectively. We prove that, for infinite additive complements A and B, if lim sup A(x)B(x)/x ≤ 1, then, for any given M > 1,...
On a constant of Turán and Erdös
On a density problem of Erdös
On a diophantine equation involving quadratic characters