Residuacity of primes (Q912886)

Let p and q be distinct odd primes with \(p=8f+1\). The author gives a delightfully simple criterion for q to be an octic residue (mod p). The criterion is given in terms of the integers a,b,c,d in the representations \(p=a^ 2+b^ 2=c^ 2+2d^ 2\) and is deduced from a variant of the Kummer-Dedekind theorem for Gaussian periods.