On the Diophantine equation x2−4pm=±yn

Let m and n be positive integers and p any odd prime. In this paper we consider the Diophantine equation x2−4pm=±yn in positive integers x and y where (x,y)=1, and we show that under some not very restrictive conditions, this equation has only finitely many solutions (x,y,m,n), and we provide a smal...

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Bibliographic Details
Published inArab journal of mathematical sciences Vol. 18; no. 2; pp. 97 - 103
Main Authors Abu Muriefah, Fadwa S., AL-Rashed, Amal
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2012
Subjects
Algebraic number
Class number
Diophantine equation
p-Adic
Class number
Algebraic number
p-Adic
Diophantine equation
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Summary:Let m and n be positive integers and p any odd prime. In this paper we consider the Diophantine equation x2−4pm=±yn in positive integers x and y where (x,y)=1, and we show that under some not very restrictive conditions, this equation has only finitely many solutions (x,y,m,n), and we provide a small explicit upper bound for n which only depends on p.
ISSN:1319-5166
DOI:10.1016/j.ajmsc.2012.01.003