if $n$ is an integer , prove that $n^4 + 4 n^2 + 11$ is of the form $16 k$.
And I went something like:
$\begin{align*} n^4 +4 n^2 +11 &= n^4 + 4 n^2 + 16 -5 \\ &= ( n^4 +4 n^2 -5) + 16 \\ &= ( n^2 +5 ) ( n^2-1) +16 \end{align*}$
So, now we have to prove that the product of $( n^2 +5 )$ and $( n^2-1)$ is a multiple of 16.
But, how can we do this? If anybody has any idea of how I can improve my solution, please share it here.