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On certain criteria for the left-primeness of entire functions. II.

THEOREM 1. Let F(z) be an entire function of finite order. Assume that for a certain constant A F(z)=A has at least one but at most finitely many simple roots and has infinitely many multiple roots all of whose multiplicities are the same. Assume further that the equations F(z)=c, F'(z)=0 have only a finite number of common roots for any cφA. Then F(z) is left-prime in entire sense. THEOREM 2. Let F(z) be such an entire function that for a constant A F(z)=A has at least one but at most finitely many simple roots and has infinitely many multiple roots all of whose multiplicities are the same. Assume that