POLYNOMIAL PELL?S EQUATION AND PERIODS OF QUADRATIC IRRATIONALS
Let be a monic quartic polynomial in where Then we show that the polynomial Pell?s equation has nontrivial solutions if and only if the values of the period of the continued fraction expansion of are 2, 4, 6,8,10,14,18and 22. Furthermore, we show that for where if the period of the continued fraction expansion of is 4, then the polynomial Pell?s equation has no nontrivial solutions
polynomial Pell?s equation.
