Related papers: Power multiples in binary recurrence sequences: an…

We continue and generalise our earlier investigations of the number of squares in binary recurrence sequences. Here we consider sequences, $\left( y_{k} \right)_{k=-\infty}^{\infty}$, arising from the solutions of generalised negative Pell…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

In Pacific J. Math. 292 (2018), 223-238, Shareshian and Woodroofe asked if for every positive integer $n$ there exist primes $p$ and $q$ such that, for all integers $k$ with $1 \leq k \leq n-1$, the binomial coefficient $\binom{n}{k}$ is…

We find a formula for the number of permutation polynomials of degree q-2 over a finite field Fq, which has q elements, in terms of the permanent of a matrix. We write down an expression for the number of permutation polynomials of degree…

We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the…

In this paper we introduce a novel notion of probabilistic bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and…

A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…

We investigate how to combine a collection of quantum binary models into a multinomial classifier. We employ a hybrid approach, adopting strategies like one-vs-one, one-vs-rest and a binary decision tree. We benchmark each method, by…

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…

We establish supercongruences for two kinds of Ap\'ery-like numbers, which involve Bernoulli numbers and Bernoulli polynomials. Conjectural supercongruences of the same type for another four kinds of Ap\'ery-like numbers are also proposed.

The Collatz conjecture is explored using polynomials based on a binary numeral system. It is shown that the degree of the polynomials, on average, decreases after a finite number of steps of the Collatz operation, which provides a weak…

Let two sequences of eventualities x (signifying the sequence, x0,x1, x2,...,xn-1) and y (signifying the sequence, y0, y1, y2,..,yn-1) both recur over the same time interval and it is required to determine whether or not a subinterval…

We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.

A method for estimating the merit factors of sequences will be provided. The result is also effective in determining the nonexistence of certain infinite collections of cyclic difference sets and cyclic matrices and associated binary…

The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to…

We give estimates from below for the greatest prime factor of the n-th term of a binary recurrence sequence.

Common intervals have been defined as a modelisation of gene clusters in genomes represented either as permutations or as sequences. Whereas optimal algorithms for finding common intervals in permutations exist even for an arbitrary number…

Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

In this article, the 2-iterated q-Appell family is introduced. Certain 2-iterated q-Appell and mixed type q-special polynomials are considered as members of this family. The numbers related to these polynomials are obtained. The determinant…