Get Math Help

Quadratic Reciprocity Theorem

Alternate names

aureum theorema | Gauss's reciprocity theorem | golden theorem | Legendre's quadratic reciprocity law | quadratic reciprocity law

Basic definition

The quadratic reciprocity theorem is a theorem that tells whether a quadratic equation modulo a prime has a solution.

Detailed definition

If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences
x^2 congruent q (mod p)
x^2 congruent p (mod q)
are both solvable or both unsolvable unless both p and q leave the remainder 3 when divided by 4 (in which case one of the congruences is solvable and the other is not).

Educational grade level

college level

Why Club Z!?

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu. Vestibulum vulputate

We're Awesome!

Vestibulum vitae aliquam nunc. Suspendisse mollis metus ac tellus egestas pharetra. Suspendisse at viverra purus. Pellentesque nec posuere ligula, eu congue leo. Integer vulputate tempor arcu.