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CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS
Published online by Cambridge University Press: 08 March 2013
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
$m$).
MSC classification
- Type
- Research Article
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- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
References
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