Lower-half quadratic-residue sum for primes congruent to seven modulo eight
= Lower-half quadratic-residue sum for primes congruent to seven modulo eight
If $p\equiv7\pmod8$, the sum of the least positive quadratic residues below $p/2$ is
$$
\frac{p^2-1}{16}.
$$
The proof uses $(\frac2p)=1$ to compare the sum of all residues with its image under doubling.