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O cechach podzielności liczb i odkrywaniu twierdzeń
(2006)
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 ...
Kształtowanie odruchów
(2006)
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 ...
Kilka uogólnień reguł pewnej gry strategicznej
(2013)
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 ...
Prime counting function π
(2013)
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 ...
Around the Wilson's theorem
(2013)
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.
O nieskończonych ciągach liczb naturalnych, parami względnie pierwszych
(2009)
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 ...
Simple proofs of some generalizations of the Wilson’s theorem
(2014)
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 ...