An Algorithm to Determine the Points with Integral Coordinates in Certain Elliptic Curves Original Research Article

We give an algorithm to determine the terms in a Lucas sequence of the first kind which are of the formktimes a square. This algorithm is applied to provide the points with integral coordinates in certain elliptic curves, as well as to solve certain exponential equations of the forman−1=b□ (wherea>1,bare given positive integers).