Say I was told to find:
$4^{1000} (mod 7)$
Since The modulo is prime, I can use fermats little theorem, now I'm just wondering if my steps are correct:
We have that:
$4^6 = 1(mod 7)$ //congruent
$1000/6 = $~166 //approx 166
$4^{1000} = (4^6)^{(166)}(4^4) $ //congruent
$= 1(4^4)(mod 7) = 4$ //congruent
Final answer = 4
I know the answer is correct, but is this the correct way of applying fermats theorem?
Any help would be much appreciated