What is the value of the following? $3^{302} \mod 5.$ I have to choose from 
a. 0 
b. 1 
c. 2 
d. 3 
e. 4
I think its e. 4 because
$$3^{302} = 3^{300} \cdot 3^2 = 3^{4\cdot 75} \cdot 3^2 = (3^4)^{75} \cdot 3^2.$$
Applying Fermat's Little Theorem to turn $3^4$ into $1$, then evaluate and solve:
$$(3^4)^{75} \cdot 3^2 \equiv 1^{75} \cdot 9  \equiv 1 \cdot 9\equiv  9 \equiv 4 \pmod 5$$ 
Can you please confirm that the answer is e. 4. Thank you. 

Hint $\ {\rm mod}\ 5\!:\,\ \color{#c00}{3^2\equiv\, -1}\ \Rightarrow\ 3^{2k}\equiv (\color{#c00}{3^2})^k\equiv (\color{#c00}{-1})^k\ $ [$\,\equiv -1\ $ if $\,k\,$ is odd, as in your case]
