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Let f, g be transcendental entire functions and p, q be nonlinear polynomials with deg p not equal 3,6. Suppose that f and p are prime and f(p(z)) = g(q(z)), then f = g circle L and p = L-1 circle q, where L is a linear polynomial. Similar results for p(f(z)) = q(g(z)) are also obtained

On the composition of a prime transcendental function and a prime polynomial