  We prove that if $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ is
a holomorphic mapping of maximal rank whose image lies in the Fermat
hypersurface of degree $d>(n+1)\max\{n-p,1\}$, then its image is contained in a
linear subspace of dimension at most $\bigg[\dfrac{n-1}{2}\bigg]$. Analog in
the logarithmic case is also given. Our result strengthens a classical result
of Green and provides a Nevanlinna theoretic proof for a recent result due to
Etesse.
