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# Variants of Korselt's Criterion

Published:2015-09-07
Printed: Dec 2015
• Thomas Wright,
Department of Mathematics, Wofford College, Spartanburg, SC 29302, USA
 Format: LaTeX MathJax PDF

## Abstract

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 $p|n$, we have $p-a|n-a$. This can be seen as a generalization of Carmichael numbers, which are integers $n$ such that $p-1|n-1$ for every $p|n$.
 Keywords: Carmichael number, pseudoprime, Korselt's Criterion, primes in arithmetic progressions
 MSC Classifications: 11A51 - Factorization; primality

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