scholarly journals Some remarks on Stolt’s Theorems for Pellian Equations

1974 ◽  
Vol 12 (1-2) ◽  
pp. 167-171 ◽  
Author(s):  
Peter Heichelheim
Keyword(s):  
Pellian Equations

A SYSTEM OF RELATIVE PELLIAN EQUATIONS AND A RELATED FAMILY OF RELATIVE THUE EQUATIONS

2006 ◽  
Vol 02 (04) ◽  
pp. 569-590 ◽  
Author(s):  
BORKA JADRIJEVIĆ ◽  
VOLKER ZIEGLER
Keyword(s):  
Number Field ◽  
Quadratic Number ◽  
Quadratic Number Field ◽  
Root Of Unity ◽  
Related Family ◽  
The Family ◽  
Thue Equation ◽  
Imaginary Quadratic Number ◽  
Pellian Equations

In this paper we consider the family of systems (2c + 1)U2 - 2cV2 = μ and (c - 2)U2 - cZ2 = -2μ of relative Pellian equations, where the parameter c and the root of unity μ are integers in the same imaginary quadratic number field [Formula: see text]. We show that for |c| ≥ 3 only certain values of μ yield solutions of this system, and solve the system completely for |c| ≥ 1544686. Furthermore we will consider the related relative Thue equation [Formula: see text] and solve it by the method of Tzanakis under the same assumptions.

scholarly journals On arithmetic progressions on Pellian equations

2007 ◽  
Vol 120 (1-2) ◽  
pp. 29-38 ◽  
Author(s):  
A. Dujella ◽  
A. Pethő ◽  
P. Tadić
Keyword(s):  
Arithmetic Progressions ◽  
Pellian Equations

Some Solutions of the Pellian Equations X 2 - Ay 2 = ± 4

1913 ◽  
Vol 15 (1/4) ◽  
pp. 157 ◽  
Author(s):  
E. E. Whitford
Keyword(s):  
Pellian Equations

scholarly journals Simultaneous Pellian equations with a single or no solution

2008 ◽  
Vol 134 (4) ◽  
pp. 369-380 ◽  
Author(s):  
Alain Togbé ◽  
Bo He
Keyword(s):  
Pellian Equations

Simultaneous Pellian equations

1988 ◽  
Vol 103 (1) ◽  
pp. 35-46 ◽  
Author(s):  
R. G. E. Pinch
Keyword(s):  
Integer Solutions ◽  
Pellian Equations ◽  
Image Position

In this paper we describe a method for finding integer solutions of simultaneous Pellian equations, that is, integer triples (x,y,z) satisfying equations of the formwhere the coefficientsa,b,c,d,fare integers and we assume thata,c, andacare not square.

scholarly journals On the extendibility of the Diophantine triple{1,5,c}

2004 ◽  
Vol 2004 (33) ◽  
pp. 1737-1746 ◽  
Author(s):  
Fadwa S. Abu Muriefah ◽  
Amal Al-Rashed
Keyword(s):  
Positive Integer ◽  
All Solutions ◽  
Recursive Sequence ◽  
Pellian Equations ◽  
Diophantine Triple

We study the problem of extendibility of the triples of the form{1,5,c}. We prove that ifck=sk2+1, where(sk)is a binary recursive sequence,kis a positive integer, and the statement that all solutions of a system of simultaneous Pellian equationsz2−ckx2=ck−1,5z2−cky2=ck−5are given by(x,y,z)=(0,±2,±sk), is valid for2≤k≤31, then it is valid for all positive integerk.

Sign in / Sign up

Export Citation Format

Share Document