In the first part of the paper the authors, using general formulas, determine and describe a class of infinite series of natural numbers pairs of which are relatively prime. The second part of the paper contains - as a ...

In the paper a set of strategy games is presented. It is shown how the “manipulative” developing of the winning strategy of a known and simple game can lead to conceptual reasoning based on reduction; then it is ...

The aim of this paper is to derive new explicit formulas for the function π, where π(x) denotes the number of primes not exceeding x. Some justifications and generalisations of the formulas obtained byWillans (1964), Minac ...

In this paper some known conditions and new congruences characterising prime numbers are given. Some of them are obtained by the generalised Wilson theorem given by Gauss. The elementary proof of this theorem is also presented.

This article attempts to single out actions performed by a person while solving a mathematical task that lead to the acquisition of desired habits towards solving such tasks. The examples of tasks, which are presented here ...

The paper contains some theorems (with proofs) from numbers divisibility theory, and suggestions how to use them in the process of teacher training, which provide good opportunities for developing students' creative ...

In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions ...

In this paper we give the necessary and sufficient conditions for the number of the form $d = k.2^7 + 1$ and $d = k.2^8 + 1$ to be divisors of the Fermat numbers $F_5$ and $F_6$, respectively. Moreover, we present numerous ...

This paper presents a structural approach to widely known numerical averages. Several equivalent conditions for a sequence to be an arithmetic sequence are formulated and prooved. Further, these conditions, expressed by ...