On the greatest prime factor of

Authors:
P. Corvaja and U. Zannier

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1705-1709

MSC (2000):
Primary 11J25

DOI:
https://doi.org/10.1090/S0002-9939-02-06771-0

Published electronically:
November 4, 2002

MathSciNet review:
1955256

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for integers , the greatest prime factor of tends to infinity with . In particular, this settles a conjecture raised by Györy, Sarkozy and Stewart, predicting the same conclusion for the product .

**[B]**Y. Bugeaud,*On the greatest prime factor of*,*Acta Arith.***86**(1998), 45-49. MR**99k:11141****[BCZ]**Y. Bugeaud, P. Corvaja, U. Zannier,*An upper bound for the G.C.D. of**and*, to appear in Math. Zeit.**[CZ]**P. Corvaja, U. Zannier,*Diophantine equations with power sums and universal Hilbert sets*,*Indagationes Math.***9**(1998), 317-332. MR**2000j:11045****[GS]**K. Györy, A. Sarkozy,*On prime factors of integers of the form*,*Acta Arith.***79**(1997). MR**98b:11030****[GSS]**K. Györy, A. Sarkozy, C.L. Stewart,*On the number of prime factors of integers of the form*,*Acta Arith.***74**(1996), 365-385. MR**97c:11091****[L]**S. Lang,, Springer-Verlag, 1983. MR*Fundamentals of Diophantine Geometry***85j:11005****[S1]**W.M. Schmidt,, Springer-Verlag LNM*Diophantine Approximation***785**, 1980. MR**81j:10038****[S2]**W.M. Schmidt,, Springer-Verlag LNM*Diophantine Approximations and Diophantine Equations***1467**, 1991. MR**94f:11059****[ST]**C.L. Stewart, R. Tijdeman,*On the greatest prime factor of*,*Acta Arith.***79**(1997). MR**98f:11101**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
11J25

Retrieve articles in all journals with MSC (2000): 11J25

Additional Information

**P. Corvaja**

Affiliation:
Dipartimento di Matematica e Informatica, via delle Scienze, 206, 33100 Udine, Italy

Email:
corvaja@dimi.uniud.it

**U. Zannier**

Affiliation:
Istituto Universitario di Architettura di Venezia - DCA, S. Croce, 191, 30135 Venezia, Italy

Email:
zannier@iuav.it

DOI:
https://doi.org/10.1090/S0002-9939-02-06771-0

Received by editor(s):
February 7, 2002

Published electronically:
November 4, 2002

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2002
American Mathematical Society