7. Find the solution to $2^{x} \equiv x^{2}(\bmod 3)$.
7. Substitute $x=2 k, 2 k+1$. $1 \equiv 2^{2 k} \equiv (2 k)^{2} \equiv k^{2}(\bmod 3), k \equiv \pm 1(\bmod 3)$, thus the positive integer $x \equiv \pm 2(\bmod 6)$ is a solution; $2 \equiv 2^{2 k+1} \equiv (2 k+1)^{2} \equiv k^{2}+k+1(\bmod 3)$, no solution.