On a one-parameter family of Riordan arrays and the weight distribution of MDS codes.
On a problem of Davenport and Schinzel
On a problem of Sidon for polynomials over finite fields
Let ω be a sequence of positive integers. Given a positive integer n, we define rₙ(ω) = |(a,b) ∈ ℕ × ℕ : a,b ∈ ω, a+b = n, 0 < a < b|. S. Sidon conjectured that there exists a sequence ω such that rₙ(ω) > 0 for all n sufficiently large and, for all ϵ > 0, . P. Erdős proved this conjecture by showing the existence of a sequence ω of positive integers such that log n ≪ rₙ(ω) ≪ log n. In this paper, we prove an analogue of this conjecture in , where is a finite field of q elements....
On a sequence arising in algebraic geometry.
On a sum involving powers of reciprocals of an arithmetical progression.
On a variant of the Erdős-Ginzburg-Ziv problem
On addition of two distinct sets of integers
What is the structure of a pair of finite integers sets A,B ⊂ ℤ with the small value of |A+B|? We answer this question for addition coefficient 3. The obtained theorem sharpens the corresponding results of G. Freiman.
On addition of two distinct sets of integers
On addition of two sets of integers
On additive properties of two special sequences
On an irreducibility theorem of I. Schur
On -sequences
Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a -sequence A satisfies . The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof of Erdős’...
On Certain Classes of Sets of Natural Numbers
On Chebyshev's polynomials and certain combinatorial identities.
On Differences and sums of Integers, II
On extremal sets without coprimes
On generalised arithmetic and geometric progressions
On generalizing the Connell sequence.
On homogeneous multiplicative hybrid problems in number theory
On integer sequences associated with the cyclic and complete graphs.