CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS

KAISA MATOMÄKI
2013 Journal of the Australian Mathematical Society  
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).
doi:10.1017/s1446788712000547 fatcat:qqsilopapvfjxc7iusylqczgmm