The Solvability of Polynomial Pell's Equation

Bal Bahadur Tamang, Ajay Singh
2020 Journal of Institute of Science and Technology  
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.
doi:10.3126/jist.v25i2.33749 fatcat:e6dsomtrpjgozgc3rxqt4tshvm