Modulo Exponential based on Fermat's little theory?

Question

I come from Computer Science background.

In order to proceed with my question, I want to clarify that we use modular exponential as part of RSA encryption; and please be warned, I'm weak at maths :)

So given the following: $165^3 \pmod{253}$, how would I be able to compute such a large number like $165^3$? and then mod that to $253$? That's just time-consuming in an exam.

So could anyone please help me with computing this much quicker?

Thanks

Answer 1

$$253=11\cdot23$$

Now $165\equiv0\pmod{11}$

$165\equiv4\pmod{23}\implies165^2\equiv4^2\pmod{23}$

$\implies165^2\cdot165\equiv4^2\cdot165\pmod{23\cdot165}$

$\equiv16\cdot165\pmod{23\cdot11}$