Define the Legendre and Jacobi symbols.

State the law of quadratic reciprocity for the Legendre symbol.

State the law of quadratic reciprocity for the Jacobi symbol, and deduce it from the corresponding result for the Legendre symbol.

Let $p$ be a prime with $p \equiv 1(\bmod 4)$. Prove that the sum of the quadratic residues in the set $\{1,2, \ldots, p-1\}$ is equal to the sum of the quadratic non-residues in this set.

For which primes $p$ is 7 a quadratic residue?