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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.
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 ...