find all the solutions: chinese remainder + fermat theorem I have following congruences, in first congruence I know I have to use the Fermat theorem for finding the solution but I couldn't understand how, because most of the samples in internet using some numbers instead of x. 
could somebody please explain it for me in simple way?
1)
$x^2 \equiv 1 \pmod{3}$
$3x \equiv 6 \pmod{15}$
2) what about the following case?
$x^3 \equiv 1 \pmod{3}$
by the way I know this link but as I said it explain by numbers.

For (1) You know by fermat's little theorem that $x$ must be coprime with $3$ and so you have $x=1,2$ and so $x  \equiv 1 \pmod 3 \space \textbf{or} \space x \equiv 2 \pmod3$ And you can even try it $1^2 \equiv 1 \pmod3$ $\space$ and $\space $ $2^2 \equiv \pmod 3$
now you have $3x \equiv 6 \pmod{15} $
And since $3,6$ and $15$ are all divisible by $3$ then You can divide the congruence by $3$ to get $x \equiv 2 \pmod5 $ Now how can you use the Chinese remainder theorem ?
