A1 Refereed original research article in a scientific journal
Carmichael numbers in arithmetic progressions
Authors: Matomaki K
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2013
Journal: Journal of the Australian Mathematical Society
Journal name in source: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
Journal acronym: J AUST MATH SOC
Number in series: 2
Volume: 94
Issue: 2
First page : 268
Last page: 275
Number of pages: 8
ISSN: 1446-7887
DOI: https://doi.org/10.1017/S1446788712000547
Abstract
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).
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).
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