On the largest prime factor of
Authors:
Florian Luca and Filip Najman
Journal:
Math. Comp. 80 (2011), 429435
MSC (2010):
Primary 11D09, 11Y50
Published electronically:
July 20, 2010
Erratum:
Math. Comp. 83 (2014), 337.
Table supplement:
supplement
MathSciNet review:
2728988
Fulltext PDF
Abstract 
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Additional Information
Abstract: In this paper, we find all integers such that has only prime factors smaller than . This gives some interesting numerical corollaries. For example, for any positive integer we can find the largest positive integer such that all prime factors of each of are less than 100.
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 R. D. Carmichael, On the numerical factors of arithmetic forms , Ann. of Math. 15 (1913), 3070. MR 1502458
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 M. Maurer, Regulator approximation and fundamental unit computation for real quadratic orders, PhD thesis, Technische Universität Darmstadt, Fachbereich Informatik, Darmstadt, Germany, 2000.
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 F. Najman, Compact representation of quadratic integers and integer points on some elliptic curves, Rocky Mountain J. Math., to appear.
 10.
 T. N. Shorey and R. Tijdeman, Generalizations of some irreducibility results by Schur, Acta Arith., to appear.
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Additional Information
Florian Luca
Affiliation:
Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, C.P. 58089, Morelia, Michoacan, Mexico
Email:
fluca@matmor.unam.mx
Filip Najman
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička Cesta 30, 10000 Zagreb, Croatia
Email:
fnajman@math.hr
DOI:
http://dx.doi.org/10.1090/S002557182010023816
Keywords:
Pell equation,
compact representation,
Lucas sequence.
Received by editor(s):
July 16, 2009
Received by editor(s) in revised form:
October 27, 2009
Published electronically:
July 20, 2010
Article copyright:
© Copyright 2010
American Mathematical Society
