Find the remainder when ${{45}^{17}}^{17}$ is divided by $204$
This question came in an examination yesterday and I couldn't solve it. The answer that was given in the solutions booklet stated this:
${{45}^{17}}^{17}$=$17k+11$= $3{k}^{'} +0=4{k}^{"}+1$ .Hence ,the remainder is 45.
I don't really understand anything stated here.
In general,is there anything I can learn for solving such types of problems based on remainders and divisibility?I would really like to learn new ways of solving such problems.
I tried searching the internet, but everything there is either too simple(elementary level) or too complex. I just learned something called the Euler's theorem, but the 2 numbers here are not coprime. :/ EDIT:Is their any way to solve this apart from sing modular arithmetic? Thank You.