Arithmetic progressions of Carmichael numbers in a reduced residue class

William D. Banks

Published 2020-10-12Version 1

Fix coprime natural numbers $a,q$. Assuming the Prime $k$-tuple Conjecture, we show that there exist arbitrarily long arithmetic progressions of Carmichael numbers, each of which lies in the reduced residue class $a$ mod $q$ and is a product of three distinct prime numbers.