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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 $$p\mid n$$.
Reviewer: Reviewer (Berlin)

##### MSC:
 11A51 Factorization; primality
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