On the residue classes of integer sequences satisfying a linear three term recurrence formula

In this paper we investigate linear three-term recurrence formulae Zn=T(n)Zn-1+U(n)Zn-2(n⩾2) with sequences of integers (T(n))n⩾0(T(n))n⩾0 and (U(n))n⩾0(U(n))n⩾0, which are ultimately periodic modulo m, e.g.(T(n)modm)n⩾0=(a0,a1,a2,…,aρ,T1,T2,…,Tw¯)(U(n)modm)n⩾0=(b0,b1,b2,…,bρ,U1,U2,…,Uw¯).In a former paper of this journal the authors computed explicitly the coefficients of a linear three-term recurrence formula for zn=Zrn+izn=Zrn+i with 0⩽i