Carmichael numbers in arithmetic progressions - Matomaki K (CAMBRIDGE UNIV PRESS, 2022)
We prove that when (a, m) = 1 and a is a quadratic residue mod m, there are infinitely many Carmichael numbers in the arithmetic progression a mod m. Indeed the number of them up to x is at least x^(1/5) when x is large enough (depending on m).