On Picard's theorem (Q681768)

In this paper, the author gives a connection/equivalence between Picard's theorem and the characterization of entire solutions of a differential equation. He proved that let \(a(z)\) be an entire function and let \(P(z)\) be a meromorphic function in \(\mathbb C\) with at least two distinct zeros, then an entire solution of the differential equation \[ f'+a(z)P(f)=0 \] must be constant. He also proves that this result and Picard's Theorem are equivalent in the sense that one implies the other.