Threshold Cryptosystem Using Pell's Equation

2011 ◽  
Author(s):  
K.V.S.S.R.S.S. Sarma ◽  
G. Santhosh Krishna Kumar ◽  
P.S. Avadhani
Keyword(s):  
Pell’S Equation ◽  
Threshold Cryptosystem

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
Sign in / Sign up

Export Citation Format

Share Document