Problem

Source: ELMO Shortlist 2012, C5

Tags: quadratics, modular arithmetic, combinatorics proposed, combinatorics



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.