 Discriminant criterion for a quadratic congruence modulo an odd prime

ID: discriminant-criterion-for-a-quadratic-congruence-modulo-an-odd-prime

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

p ∤ a

, the congruence

a X^{2} + b X + c = 0 (mod p)

has a solution exactly when its discriminant

b^{2} - 4 a c

p

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