Strong uniqueness polynomials of degree 6 and unique range sets for powers of meromorphic functions

We investigate the uniqueness problems for meromorphic functions with higher multiplicities of zeros and poles. As a consequence, we present a class of strong uniqueness polynomials for meromorphic functions (SUPM) of degree 6. We also proved that there exist the sets S of seven elements such that for arbitrary two meromorphic functions f and g, the condition E-fd(S) = E(g)d (S), with d >= 2, implies f = xi g, where xi is a root of unity of degree d.