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FACTORS OF CARMICHAEL NUMBERS AND A WEAK $k$-TUPLES CONJECTURE

Part of: Elementary number theory

Published online by Cambridge University Press:  17 November 2015

THOMAS WRIGHT
THOMAS WRIGHT*
Affiliation:
Department of Mathematics, Wofford College, 429 N. Church St., Spartanburg, SC 29302, USA email [email protected]
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Abstract

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In light of the recent work by Maynard and Tao on the Dickson $k$-tuples conjecture, we show that with a small improvement in the known bounds for this conjecture, we would be able to prove that for some fixed $R$, there are infinitely many Carmichael numbers with exactly $R$ factors for some fixed $R$. In fact, we show that there are infinitely many such $R$.

Keywords

Carmichael numbersDickson’s conjectureprime k-tuplespseudoprimes

MSC classification

Primary: 11A51: Factorization; primality
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 3 , June 2016 , pp. 421 - 429
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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