Pell’s Equation, Superirregularity and Randomness

2014 ◽  
pp. 251-369
Author(s):  
József Beck
Keyword(s):  
Pell’S Equation

The Solvability of Polynomial Pell’s Equation

2020 ◽  
Vol 25 (2) ◽  
pp. 125-132
Author(s):  
Bal Bahadur Tamang ◽  
Ajay Singh
Keyword(s):  
Trivial Solution ◽  
Continued Fraction ◽  
Laurent Series ◽  
Quadratic Polynomial ◽  
Continued Fraction Expansion ◽  
Pell’S Equation ◽  
Integer Polynomials

This article attempts to describe the continued fraction expansion of ÖD viewed as a Laurent series x-1. As the behavior of the continued fraction expansion of ÖD is related to the solvability of the polynomial Pell’s equation p2-Dq2=1  where D=f2+2g  is monic quadratic polynomial with deg g<deg f  and the solutions p, q  must be integer polynomials. It gives a non-trivial solution if and only if the continued fraction expansion of ÖD  is periodic.

scholarly journals Midpoint criteria for solving Pell’s equation using the nearest square continued fraction

2010 ◽  
Vol 79 (269) ◽  
pp. 485-485 ◽  
Author(s):  
Keith Matthews ◽  
John Robertson ◽  
Jim White
Keyword(s):  
Continued Fraction ◽  
Pell’S Equation

Pell's Equation: A Tool for the Puzzle-Smith

1987 ◽  
Vol 71 (458) ◽  
pp. 261 ◽  
Author(s):  
Mogens Esrom Larsen
Keyword(s):  
Pell’S Equation

General Pell’s Equation

2015 ◽  
pp. 55-105
Author(s):  
Titu Andreescu ◽  
Dorin Andrica
Keyword(s):  
Pell’S Equation

scholarly journals Units of Real Quadratic Fields

1971 ◽  
Vol 44 ◽  
pp. 51-55 ◽  
Author(s):  
Akira Takaku
Keyword(s):  
Positive Solution ◽  
Quadratic Fields ◽  
Pell’S Equation ◽  
Real Quadratic Fields ◽  
Real Quadratic

1. Let D be a positive square-free integer. Throughout this note we shall use the following notations;d = d(D): the discriminant of ,t0, u0: the least positive solution of Pell’s equation t2 — du2 = 4,

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