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Integers


Mathematical Citation Quotient (MCQ) 2017: 0.20

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1867-0660
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On the Equation ax x (mod b)

Jam Germain
  • Département de mathématiques et de statistiques, Université de Montréal, Pav. André-Aisenstadt, Bureau 5190 2920, Chemin de la Tour, Montréal, Québec H3T 1J4, Montréal, Canada. E-mail:
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Published Online: 2010-01-26 | DOI: https://doi.org/10.1515/INTEG.2009.050

Abstract

Recently Jiménez-Urroz and Yebra [On the Equation ax x (mod bn )] constructed, for any given a and b, solutions x to the title equation. Moreover they showed how these can be lifted to higher powers of b to obtain a b-adic solution for certain integers b. In this paper we find all positive integer solutions x to the title equation, proving that, for given a and b, there are X/b + Ob (1) solutions xX. We also show how solutions may be lifted in more generality. Moreover we show that the construction of [Jiménez-Urroz and Yebra, On the Equation ax x (mod bn )] (and obvious modifications) cannot always find all solutions to ax x (mod b).

Keywords.: Congruence; solutions

About the article

Received: 2008-10-30

Revised: 2009-08-12

Accepted: 2009-08-22

Published Online: 2010-01-26

Published in Print: 2009-12-01


Citation Information: Integers, Volume 9, Issue 6, Pages 629–638, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2009.050.

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