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Proceedings of the American Mathematical Society
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On the diophantine equation $x^{2}=4q^{m}-4q^{n}+1$

Author(s): Florian Luca
Journal: Proc. Amer. Math. Soc. 131 (2003), 1339-1345.
MSC (2000): Primary 11D61, 11D72
Posted: December 6, 2002
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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.


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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

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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

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C. Skinner, The diophantine equation $x^{2}=4q^{n}-4q+1$, Pacific J. of Math. 139 no. 2 (1989), 303-309. MR 90g:11039

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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


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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: 10.1090/S0002-9939-02-06921-6
PII: S 0002-9939(02)06921-6
Received by editor(s): September 28, 2001
Posted: December 6, 2002
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2002, American Mathematical Society


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