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ON CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS

Part of: Multiplicative number theory Elementary number theory Computational number theory

Published online by Cambridge University Press:  26 April 2010

WILLIAM D. BANKS  and
CARL POMERANCE
WILLIAM D. BANKS*
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (email: bankswd@missouri.edu)
CARL POMERANCE
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, USA (email: carl.pomerance@dartmouth.edu)
*
✉For correspondence; e-mail: bankswd@missouri.edu
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Abstract

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Assuming a conjecture intermediate in strength between one of Chowla and one of Heath-Brown on the least prime in a residue class, we show that for any coprime integers a and m≥1, there are infinitely many Carmichael numbers in the arithmetic progression a mod m.

Keywords

Carmichael numberarithmetic progression

MSC classification

Secondary: 11N13: Primes in progressions 11A51: Factorization; primality 11N25: Distribution of integers with specified multiplicative constraints 11Y11: Primality
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 3 , June 2010 , pp. 313 - 321
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The second author was supported in part by NSF grant DMS-0703850.

References

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