last two digits of $14^{5532}$? This is a exam question, something related to network security, I have no clue how to solve this!
Last two digits of $7^4$ and $3^{20}$ is $01$, what is the last two digits of $14^{5532}$?

${\rm mod}\,\ \color{#c00}{25}\!:\, \ 14\equiv 8^{\large 2}\Rightarrow\, 14^{\large 10}\equiv \overbrace{8^{\large 20}\equiv 1}^{\rm\large  Euler\ \phi}\,\Rightarrow\, \color{#0a0}{14^{\large 1530}}\equiv\color{#c00}{\bf 1}$ 
${\rm mod}\ 100\!:\,\ 14^{\large 2}\, \color{#0a0}{14^{\large 1530}} \equiv  14^{\large 2} (\color{#c00}{{\bf 1}\!+\!25k}) \equiv  14^{\large 2} \equiv\, 96$
