Simultaneous primality of the integers n and 2n-d
A necessary and sufficient condition for the simultaneous primality of integers $n$ and $2n-d$ is given by means of congruences ${\rm mod}\,{n(2n-d)}$ that hold if and only if they form a prime pair. These are used to obtain explicit primality criteria for some values of $d$, after computation of a...
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Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2013-11-01
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| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/148 |
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doaj-5f791e48d55c4cb2be2941e9f00a46ca2020-11-24T22:30:19ZdeuWydawnictwo Naukowe Uniwersytetu PedagogicznegoAnnales Universitatis Paedagogicae Cracoviensis: Studia Mathematica 2081-545X2300-133X2013-11-01128390Simultaneous primality of the integers n and 2n-dFlavio TorassoA necessary and sufficient condition for the simultaneous primality of integers $n$ and $2n-d$ is given by means of congruences ${\rm mod}\,{n(2n-d)}$ that hold if and only if they form a prime pair. These are used to obtain explicit primality criteria for some values of $d$, after computation of a finite number of exceptions that appear when $n$ is lower than a fixed quantity depending only on $d$.http://studmath.up.krakow.pl/index.php/studmath/article/view/148 |
| collection |
DOAJ |
| language |
deu |
| format |
Article |
| sources |
DOAJ |
| author |
Flavio Torasso |
| spellingShingle |
Flavio Torasso Simultaneous primality of the integers n and 2n-d Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| author_facet |
Flavio Torasso |
| author_sort |
Flavio Torasso |
| title |
Simultaneous primality of the integers n and 2n-d |
| title_short |
Simultaneous primality of the integers n and 2n-d |
| title_full |
Simultaneous primality of the integers n and 2n-d |
| title_fullStr |
Simultaneous primality of the integers n and 2n-d |
| title_full_unstemmed |
Simultaneous primality of the integers n and 2n-d |
| title_sort |
simultaneous primality of the integers n and 2n-d |
| publisher |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego |
| series |
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| issn |
2081-545X 2300-133X |
| publishDate |
2013-11-01 |
| description |
A necessary and sufficient condition for the simultaneous primality of integers $n$ and $2n-d$ is given by means of congruences ${\rm mod}\,{n(2n-d)}$ that hold if and only if they form a prime pair. These are used to obtain explicit primality criteria for some values of $d$, after computation of a finite number of exceptions that appear when $n$ is lower than a fixed quantity depending only on $d$. |
| url |
http://studmath.up.krakow.pl/index.php/studmath/article/view/148 |
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AT flaviotorasso simultaneousprimalityoftheintegersnand2nd |
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