Factorization of entire solutions of some algebraic differential equations

We investigate the factorization of entire solutions of the following algebraic differential equations: bn(z)f in(f )jn + bn−1(z)f in−1(f )jn−1 +···+b0(z)f i0(f )j0 = b(z), where n ∈ N is a natural number, is 0, js 0, is + js > 0 (0 s n) are the integers, and bi (z) ≡ 0 (0 i n) are the polynomials.Moreover, the results enable us to provide new criteria/proofs of primeness or pseudo-primeness for certain well-known classes of entire functions. © 2005 Elsevier Inc. All rights reserved