BALANCING WITH POWERS OF THE LUCAS SEQUENCE OF RECURRENCE un = Aun-1-un-2.

In this paper, we show that there is no solution of the diophantine equation uk1+ uk2 +...+ukn-1 = uln+1+uln+2+...+uln+rr for special cases of k and l where the elements of sequence fung satisfy the relation un = Aun-1 - un-2 with u0 = 0, u1= 1 and A ≥ 3 is a positive integer. [ABSTRACT FROM AUTHOR]