ELMO SL 2012 C5

Form the infinite graph $A$ by taking the set of primes $p$ congruent to $1\pmod{4}$ , and connecting $p$ and $q$ if they are quadratic residues modulo each other. Do the same for a graph $B$ with the primes $1\pmod{8}$ . Show $A$ and $B$ are isomorphic to each other.

Linus Hamilton.