On the largest prime factor of

Authors:
Florian Luca and Filip Najman

Journal:
Math. Comp. **80** (2011), 429-435

MSC (2010):
Primary 11D09, 11Y50

DOI:
https://doi.org/10.1090/S0025-5718-2010-02381-6

Published electronically:
July 20, 2010

Erratum:
Math. Comp. 83 (2014), 337.

Table supplement:
supplement

MathSciNet review:
2728988

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Abstract | References | Similar Articles | 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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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:
https://doi.org/10.1090/S0025-5718-2010-02381-6

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