Quadratic residues and Legendre symbol
General · Mathematics
Study notes
Q: Is 2 a quadratic residue mod 7? Compute (2/7) and (3/7). Squares mod 7: 1²=1, 2²=4, 3²=2, 4²=2, 5²=4, 6²=1: QRs {1,2,4}. 2 ∈ {1,2,4}: YES, (2/7) = 1 (3² = 9 ≡ 2 ✓!). 3 ∉ {1,2,4}: NO, (3/7) = -1. Euler check: 2³ = 8 ≡ 1 ✓; 3³ = 27 ≡ 6 ≡ -1 ✓!