Let f,
g be transcendental entire functions
and p, q be nonlinear polynomials with deg p≠3,6. Suppose
that f and p are prime and f(p(z)) = g(q(z)), then f =
g∘L and
p = L−1∘q, where L is a
linear polynomial. Similar results for p(f(z)) = q(g(z)) are also obtained.