The Quadratic Character of 2
Rafael Jakimczuk · Mathematics Magazine · 2011
SummaryThe number 2 is a quadratic residue mod p if p = 8k + 1 or p = 8k + 7, but not if p = 8k + 3 or p = 8k + 5. This is proved by a simple counting argument, assuming the existence of a primitive root mod p.