Closed formulae for certain Fermat–Pell equations
Closed formulae for certain Fermat–Pell equations
Given positive integers j, k, with j≥2, we show that there are positive integers d, e such that d has continued fraction expansion d=[e,k,…,k,2e¯], with period j, if and only if k is even or 3∤j, in which case we give closed formulae to find all such d, e as …