an:06527795
Zbl 1378.11017
Wright, Thomas
Variants of Korselt's criterion
EN
Can. Math. Bull. 58, No. 4, 869-876 (2015).
00350504
2015
j
11A51
Carmichael number; pseudoprime; Korselt's criterion; primes in arithmetic progressions
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 \(p\mid n\).