We present an application of difference equations to number theory by considering the set of linear second-order recursive relations,Un+2( √ R,Q) =RUn+1 −QUn,U0 = 0,U1 = 1, and Vn+2( √ R,Q) =RVn+1 −QVn, V0 = 2,V1 = √ R, where R and Q are relatively prime integers and n∈ {0,1, . . .}. These equations describe the set of extended Lucas sequences, or rather, the Lehmer sequences. We add that the r...