Cubic Pell Equations

2018 ◽  
pp. 205-245
Author(s):  
Samuel A. Hambleton ◽  
Hugh C. Williams
Keyword(s):  
Pell Equations

scholarly journals Solution of certain Pell equations

2018 ◽  
Vol 11 (04) ◽  
pp. 1850056 ◽  
Author(s):  
Zahid Raza ◽  
Hafsa Masood Malik
Keyword(s):  
Positive Integer ◽  
Fundamental Solution ◽  
Positive Solutions ◽  
Continued Fraction ◽  
Pell Equation ◽  
Lucas Sequences ◽  
Pell Equations ◽  
Integer Solutions ◽  
Positive Integers

Let [Formula: see text] be any positive integers such that [Formula: see text] and [Formula: see text] is a square free positive integer of the form [Formula: see text] where [Formula: see text] and [Formula: see text] The main focus of this paper is to find the fundamental solution of the equation [Formula: see text] with the help of the continued fraction of [Formula: see text] We also obtain all the positive solutions of the equations [Formula: see text] and [Formula: see text] by means of the Fibonacci and Lucas sequences.Furthermore, in this work, we derive some algebraic relations on the Pell form [Formula: see text] including cycle, proper cycle, reduction and proper automorphism of it. We also determine the integer solutions of the Pell equation [Formula: see text] in terms of [Formula: see text] We extend all the results of the papers [3, 10, 27, 37].

scholarly journals On the number of solutions of simultaneous Pell equations

2002 ◽  
Vol 101 (3) ◽  
pp. 215-221 ◽  
Author(s):  
Pingzhi Yuan
Keyword(s):  
Number Of Solutions ◽  
Pell Equations ◽  
Simultaneous Pell Equations

Orthogonal-type polynomials and Pell equations

2013 ◽  
Vol 24 (10) ◽  
pp. 796-806 ◽  
Author(s):  
James C. Griffin ◽  
Gajath Gunatillake
Keyword(s):  
Pell Equations

Common Solutions of Two Simultaneous Pell Equations

1922 ◽  
Vol 23 (4) ◽  
pp. 307 ◽  
Author(s):  
A. Arwin
Keyword(s):  
Pell Equations ◽  
Simultaneous Pell Equations

scholarly journals Arithmetic progressions on Pell equations

2008 ◽  
Vol 128 (6) ◽  
pp. 1389-1409 ◽  
Author(s):  
A. Pethő ◽  
V. Ziegler
Keyword(s):  
Arithmetic Progressions ◽  
Pell Equations

scholarly journals Solving Families of Simultaneous Pell Equations

1997 ◽  
Vol 67 (2) ◽  
pp. 246-251 ◽  
Author(s):  
Michael A Bennett
Keyword(s):  
Pell Equations ◽  
Simultaneous Pell Equations

scholarly journals On the number of solutions to systems of Pell equations

2007 ◽  
Vol 125 (2) ◽  
pp. 356-392 ◽  
Author(s):  
Mihai Cipu ◽  
Maurice Mignotte
Keyword(s):  
Number Of Solutions ◽  
Pell Equations
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