Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the diophantine equation $x^{2}=4q^{m}-4q^{n}+1$


Author: Florian Luca
Journal: Proc. Amer. Math. Soc. 131 (2003), 1339-1345
MSC (2000): Primary 11D61, 11D72
DOI: https://doi.org/10.1090/S0002-9939-02-06921-6
Published electronically: December 6, 2002
MathSciNet review: 1949862
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we find all positive integer solutions $(x,q,m,n)$ of the diophantine equation from the title with $q$ a prime power.


References [Enhancements On Off] (What's this?)

  • 1. Y. Bilu, G. Hanrot, P. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers, J. Reine Angew. Math. 539 (2001), 75-122. MR 2002j:11027
  • 2. M. H. Le, The diophantine equation $x^{2}=4q^{m}+4q^{n}+1$, Proc. Amer. Math. Soc. 106 no. 3 (1989), 599-604. MR 90b:11024
  • 3. M. Mignotte, A. Petho, On the diophantine equation $x^{p}-x=y^{q}-y$, Publ. Math. 43 no. 1 (1999), 207-216. MR 2000d:11044
  • 4. C. Skinner, The diophantine equation $x^{2}=4q^{n}-4q+1$, Pacific J. of Math. 139 no. 2 (1989), 303-309. MR 90g:11039
  • 5. N. Tzanakis, J. Wolfskill, The diophantine equation $x^{2}=4q^{a/2}+4q+1$, with an application to coding theory, J. Number Theory 26 no. 1 (1987), 96-116. MR 88g:11009

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11D61, 11D72

Retrieve articles in all journals with MSC (2000): 11D61, 11D72


Additional Information

Florian Luca
Affiliation: Instituto de Matemáticas UNAM, Ap. Postal 61-3 (Xangari), CP 58 089, Morelia, Michoacán, Mexico
Email: fluca@matmor.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-02-06921-6
Received by editor(s): September 28, 2001
Published electronically: December 6, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society