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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Perfect repdigits


Authors: Kevin Broughan, Sergio Guzman Sanchez and Florian Luca
Journal: Math. Comp. 82 (2013), 2439-2459
MSC (2010): Primary 11A63, 11A05, 11A25
Published electronically: March 18, 2013
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Abstract: Here, we give an algorithm to detect all perfect repdigits in any base $ g>1$. As an application, we find all such examples when $ g\in [2,\ldots ,333]$, extending a calculation from [2]. In particular, we demonstrate that there are no odd perfect repdigits for this range of bases.


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Additional Information

Kevin Broughan
Affiliation: Department of Mathematics, University of Waikato, Hamilton 3216, New Zealand
Email: kab@waikato.ac.nz

Sergio Guzman Sanchez
Affiliation: Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
Email: sguzman@matmor.unam.mx

Florian Luca
Affiliation: Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
Email: fluca@matmor.unam.mx

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02682-8
PII: S 0025-5718(2013)02682-8
Keywords: Perfect numbers, repdigits, Pell equations, Lucas sequences
Received by editor(s): March 3, 2011
Received by editor(s) in revised form: June 9, 2011, August 9, 2011, September 5, 2011, December 14, 2011, December 22, 2011, January 11, 2012, and January 24, 2012
Published electronically: March 18, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.