Geodesic
Variants of Korselt’s Criterion
Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 869-876

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DOI

Under sufficiently strong assumptions about the first term in an arithmetic progression, we prove that for any integer $a$ , there are infinitely many $n\,\in \,\mathbb{N}$ such that for each prime factor $p\,\text{ }\!\!|\!\!\text{ }\,n$ , we have $p\,-\,a\,\text{ }\!\!|\!\!\text{ }\,n\,-\,a$ . This can be seen as a generalization of Carmichael numbers, which are integers $n$ such that $p\,-\,1\,\text{ }\!\!|\!\!\text{ }\,n\,-\,1$ for every $p\,\text{ }\!\!|\!\!\text{ }\,n$ .
DOI : 10.4153/CMB-2015-027-3
Mots-clés : 11A51, Carmichael number, pseudoprime, Korselt’s Criterion, primes in arithmetic progressions 
Wright, Thomas. Variants of Korselt’s Criterion. Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 869-876. doi: 10.4153/CMB-2015-027-3
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     author = {Wright, Thomas},
     title = {Variants of {Korselt{\textquoteright}s} {Criterion}},
     journal = {Canadian mathematical bulletin},
     pages = {869--876},
     year = {2015},
     volume = {58},
     number = {4},
     doi = {10.4153/CMB-2015-027-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-027-3/}
}
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