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Variants of Korselt’s criterion. (English) Zbl 1378.11017
Summary: 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 \(p\mid n\), we have \(p-a\mid n-a\). This can be seen as a generalization of Carmichael numbers, which are integers \(n\) such that \(p-1\mid n-1\) for every \(p\mid n\).

MSC:
11A51 Factorization; primality
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