Open AccessOn the Diophantine equation x2−4pm=±yn
Author(s) -
Fadwa S. Abu Muriefah,
Amal Al-Rashed
Publication year - 2012
Publication title -
arab journal of mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 11
eISSN - 2588-9214
pISSN - 1319-5166
DOI - 10.1016/j.ajmsc.2012.01.003
Subject(s) - mathematics , diophantine equation , prime (order theory) , upper and lower bounds , finitely generated abelian group , discrete mathematics , combinatorics , pure mathematics , mathematical analysis
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
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom