On the problem of uniqueness for the maximum Stirling number(s) of the second kind.
On the product of balanced sequences
The product w = u ⊗ v of two sequences u and v is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product w of two balanced sequences u,v is balanced too. In the case u and v are binary sequences, we prove, as a main result, that, if such a product w is balanced and deg(w) = 4, then w is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems...
On the product of balanced sequences
The product w = u ⊗ v of two sequences u and v is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product w of two balanced sequences u,v is balanced too. In the case u and v are binary sequences, we prove, as a main result, that, if such a product w is balanced and deg(w) = 4, then w is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems...
On the Product of Consecutive Elements of an Arithmetic Progression.
On the q-log-Concavity of Gaussian Binomial Coefficients.
On the quartic character of quadratic units.
On the quartic character of quadratic units
Let ℤ be the set of integers, and let (m,n) be the greatest common divisor of integers m and n. Let p be a prime of the form 4k+1 and p = c²+d² with c,d ∈ ℤ, and c ≡ d₀ ≡ 1 (mod 4). In the paper we determine for p = x²+(b²+4α)y² (b,x,y ∈ ℤ, 2∤b), and for p = x²+(4a²+1)y² (a,x,y∈ℤ) on the condition that (c,x+d) = 1 or (d₀,x+c) = 1. As applications we obtain the congruence for and the criterion for (if p ≡ 1 (mod 8)), where Uₙ is the Lucas sequence given by U₀ = 0, U₁ = 1 and , and b ≢...
On the quotient sequence of sequences of integers
On the Real Roots of Euler Polynomials.
On the real roots of generalized Thue-Morse polynomials
On the recognizability of self-generating sets.
On the representation of 1,2,..., n by sums
On the representation of integers as sums of distinct terms from a fixed set
On the representation of large integers as sums of distinct summands taken from a fixed set
On the representation of as .
On the resolution of index form equations in dihedral quartic number fields.
On the roots of certain sequences of congruences
On the set of numbers {14, 22, 30, 42, 90}
On the size of dissociated bases.
On the solutions of diophantine equations in units