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Variants of Korselt’s Criterion

Published online by Cambridge University Press:  20 November 2018

Thomas Wright
Thomas Wright*
Affiliation:
Department of Mathematics, Wofford College, Spartanburg, SC 29302, USA e-mail: wrighttj@wofford.edu
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Abstract

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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 $p\,\text{ }\!\!|\!\!\text{ }\,n$ .

Keywords

11A51Carmichael numberpseudoprimeKorselt’s Criterion, primes in arithmetic progressions

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 4 , 01 December 2015 , pp. 869 - 876
Copyright
Copyright © Canadian Mathematical Society 2015

References

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