how about:
n^4 + 4 = n^4 + 4 - 4n^2 + 4n^2 = (n^2 + 2)^2 - (2n)^2 = (n^2 + 2n + 2)(n^2 - 2n + 2)
:)
edit:
sorry, i pulled up an old post... just realized that it's from April not May 20th...
after combining the logs, try to prove that
\frac{1}{x} \geq \ln (1 + \frac{1}{x})
for all positive x
edit:
oops i missed the last reply while typing mine sorry