On the Diophantine equationAx2+22m=yn-Reference-Cited by-同舟云学术

On the Diophantine equationAx2+22m=yn

Published:2001 Issue:6 Volume:25 Page:373-381
ISSN:0161-1712
Container-title:International Journal of Mathematics and Mathematical Sciences
language:en
Short-container-title:International Journal of Mathematics and Mathematical Sciences

Author:

Abu Muriefah Fadwa S.¹

Affiliation:

1. Girls College of Education, Science Sections (Mathematics), Sitten Street, Al Malaz, P.O. Box 27104, Riyadh, Saudi Arabia

Abstract

Lethdenote the class number of the quadratic fieldℚ(−A)for a square free odd integerA>1, and suppose thatn>2is an odd integer with(n,h)=1andm>1. In this paper, it is proved that the equation of the title has no solution in positive integersxandyifnhas any prime factor congruent to 1 modulo 4. Ifnhas no such factor it is proved that there exists at most one solution withxandyodd. The casen=3is solved completely. A result of E. Brown forA=3is improved and generalized to the case whereAis a prime≢7(mod8).

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Link

http://downloads.hindawi.com/journals/ijmms/2001/312951.pdf

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