How did we find the solution? In my lecture notes, I read that "We know that $$x^2 \equiv 2 \pmod {7^3}$$ has as solution $$x \equiv 108 \pmod {7^3}$$"
How did we find this solution? 
Any help would be appreciated!

For example, $3^2=2\bmod 7$. So $(3+7k)^2=2+7+42k\bmod 7^2$. So $k=1$ and $10^2=2\bmod 7^2$. So $(10+7^2h)^2=2+2\cdot7^2(1+10h)\bmod 7^3$. So $h=2$. Bother! Is the crummy formatting my fault or the iPhone 6+ ?
