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- Title
CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS.
- Authors
MATOMÄKI, KAISA
- Abstract
We prove that when $(a, m)= 1$ and $a$ is a quadratic residue $\hspace{0.167em} \mathrm{mod} \hspace{0.167em} m$, there are infinitely many Carmichael numbers in the arithmetic progression $a\hspace{0.167em} \mathrm{mod} \hspace{0.167em} m$. Indeed the number of them up to $x$ is at least ${x}^{1/ 5} $ when $x$ is large enough (depending on $m$).
- Subjects
ARITHMETIC series; CONGRUENCES &; residues; INTEGERS; ABELIAN groups; UNIFORM distribution (Probability theory)
- Publication
Journal of the Australian Mathematical Society, 2013, Vol 94, Issue 2, p268
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788712000547