How to decode fast RSA with prime number in base

Question

I want to decode $13^3$ (mod 34) but I have

$13^3 \equiv 13^2*13 \equiv (-1)^2 *13$ (mod 34)

and I'm stuck the answer is 21

I know I can $13^3 \equiv $ (mod 34) so $13^3=2197$
$13^3/34=2197/34=64$

and $2197 - 34*64 = 21 $

Answer 1

Note that you are wrong, as $13^2 \equiv -1 \not \equiv (-1)^2 \pmod {34}$. Note that $$13^{3} \equiv 13^2 \times 13 \equiv 169 \times 13 \equiv (-1) \times 13 \equiv -13 \equiv 21 \pmod {34}$$