Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 4, Tome 67 (1977), pp. 167-183
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Yu. V. Matiyasevich. A class of primality criteria formulated in terms of the divisibility of binomial coefficients. Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 4, Tome 67 (1977), pp. 167-183. http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a8/
@article{ZNSL_1977_67_a8,
author = {Yu. V. Matiyasevich},
title = {A class of primality criteria formulated in terms of the divisibility of binomial coefficients},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {167--183},
year = {1977},
volume = {67},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a8/}
}
TY - JOUR
AU - Yu. V. Matiyasevich
TI - A class of primality criteria formulated in terms of the divisibility of binomial coefficients
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1977
SP - 167
EP - 183
VL - 67
UR - http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a8/
LA - ru
ID - ZNSL_1977_67_a8
ER -
%0 Journal Article
%A Yu. V. Matiyasevich
%T A class of primality criteria formulated in terms of the divisibility of binomial coefficients
%J Zapiski Nauchnykh Seminarov POMI
%D 1977
%P 167-183
%V 67
%U http://geodesic.mathdoc.fr/item/ZNSL_1977_67_a8/
%G ru
%F ZNSL_1977_67_a8
We find a class of theorems of the type "$q$ is a prime number iff $R(g)$ is a divisor of the binomial coefficient $\begin{pmatrix}S(q)\\T(q)\end{pmatrix}$"; here $R$, $S$, $T$ are certain fully significant functions that are superpositions of addition, subtraction, multiplication, division, and raising to a power. Similar criteria were also obtained for prime Mersenne numbers, prime Fermat numbers, and twin-prime numbers.
