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.

the answer is any x =2+5(3k) or x=2+5(1+3k). For the second equation gives 
x-2=5k or x=2+5k and upon squaring we get k=0 or 1 mod 3. The result follows.
