Open AccessThe Solvability of Polynomial Pell’s Equation
Author(s) -
Bal Bahadur Tamang,
Ajay Kumar Singh
Publication year - 2020
Publication title -
journal of institute of science and technology
Language(s) - English
Resource type - Journals
eISSN - 2467-9240
pISSN - 2467-9062
DOI - 10.3126/jist.v25i2.33749
Subject(s) - monic polynomial , mathematics , continued fraction , fraction (chemistry) , polynomial , laurent series , quadratic equation , integer (computer science) , laurent polynomial , combinatorics , stable polynomial , matrix polynomial , solving quadratic equations with continued fractions , pure mathematics , quadratic function , discrete mathematics , mathematical analysis , alternating polynomial , binary quadratic form , arithmetic , computer science , geometry , chemistry , organic chemistry , remainder , programming language
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.