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The Solvability of Polynomial Pell's Equation
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