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On the least primitive root modulo 2p for odd primes p

Paszkiewicz A.

Electronics and Telecommunications Quarterly

2009

Vol. 55, No 4

649-658

In this paper we present results of numerical investigations concerning primitive roots modulo m = 2p, where p is prime greater than 2. This is one of these cases of integers m for which the multiplicative group of primitive rests modulo m can be generated by one element. Our computations comprise all primes below 10 10 .

On the average of the least quadratic non-residue modulo a prime number

Paszkiewicz A.

Electronics and Telecommunications Quarterly

2009

Vol. 55, No 4

639-647

In this paper we focus on a problem of existence the mean value of the least quadratic non-residue modulo a prime number. We prove that the answer to that question is positive and calculate the exact value of that constant with high accuracy. We also prove that the density of all primes having its least quadratic non-residue equal to k-th prime is 1/2k. Some computational results are included to provide numerical arguments that the convergence is very fast.

Modulo arithmetic and modulo design

Zdráhal T.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

447-450

This paper deals with one application of Modular Arithmetic intended to students of secondary schools. The method of creating so called modulo designs by means of modulo numbers is shown. The designs can be created by means of the Cabri Geometry.This access enables pupils to develop effectively their creative thinking within not only mathematics.

Arytmetyka zredukowanego systemu binarnego

Ulman Z., Plebanek M., Ożarowski M.

Pomiary Automatyka Kontrola

2007

R. 53, nr 4

76-79

Arytmetyka zredukowanego systemu binarnego umożliwia wykonywanie operacji modulo w binarnych układach logicznych liczących modulo . Z tego powodu jest ona chętnie stosowana w algorytmach cyfrowego przetwarzania sygnałów, na przykład do obliczeń transformaty Fouriera modulo liczby Fermata. W literaturze polskiej system ten nie był dotychczas omawiany. Artykuł przedstawia szczegółową definicję zredukowanego systemu binarnego oraz przedstawia zasady wykonywania elementarnych operacji arytmetycznych w układach cyfrowych.

Diminished-1 arithmetic makes possible performing modulo-2n+1 operations in binary arithmetic hardware which computes modulo-2n. For this reason it is willingly used in various digital signal processing applications, for instance in computing modulo-Fermat-number Fourier transforms. In this article the definition of the diminished-1 system is discussed in detail in comparison to the natural binary system. Basic arithmetic diminished-1 operations in binary circuits are also considered.