Carmichael numbers in arithmetic progressions

: Matomaki K

Publisher: CAMBRIDGE UNIV PRESS

: 2013

: Journal of the Australian Mathematical Society

: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY

: J AUST MATH SOC

: 2

: 94

: 2

: 268

: 275

: 8

: 1446-7887

DOI: https://doi.org/10.1017/S1446788712000547

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).

CarmichaelAPs.pdf