摘要： In this paper, we use the theory of value distribution and study the uniqueness of meromorphic functions. We will prove the following result: Let f(z) and g(z) be two transcendental meromorphic functions, p(z) a polynomial of degree k, n≥max{11, k+1} a positive integer. If fn(z)f(z) and gn(z)g(z) share p(z)CM, then either f(z)=c1ecp(z)dz, g(z)=c2ecp(z)dz ,where c1, c2 and c are three constants satisfying (c1c2)n+1c2=-1 or f(z)≡tg(z) for a constant t such that tn+1=1.
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