TY - JOUR AU - Tamang, Bal Bahadur AU - Singh, Ajay PY - 2020/12/25 Y2 - 2024/03/29 TI - The Solvability of Polynomial Pell’s Equation JF - Journal of Institute of Science and Technology JA - J. Inst. Sci. Tech. VL - 25 IS - 2 SE - Note DO - 10.3126/jist.v25i2.33749 UR - https://www.nepjol.info/index.php/JIST/article/view/33749 SP - 125-132 AB - <p>This article attempts to describe the continued fraction expansion of ÖD viewed as a Laurent series x<sup>-1</sup>. As the behavior of the continued fraction expansion of ÖD&nbsp;is related to the solvability of the polynomial Pell’s equation p<sup>2</sup>-Dq<sup>2</sup>=1&nbsp; where D=f<sup>2</sup>+2g&nbsp; is monic quadratic polynomial with deg g&lt;deg f&nbsp; and the solutions p, q&nbsp; must be integer polynomials. It gives a non-trivial solution if and only if the continued fraction expansion of ÖD&nbsp; is periodic.</p> ER -