Also called the Aureum Theorema (Golden Theorem) by Gauß. If and are distinct Odd Primes, then the Congruences
See also Jacobi Symbol, Kronecker Symbol, Legendre Symbol, Quadratic Residue, Reciprocity Theorem
References
Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.
Oxford, England: Oxford University Press, p. 39, 1996.
Ireland, K. and Rosen, M. ``Quadratic Reciprocity.'' Ch. 5 in A Classical Introduction to Modern Number Theory, 2nd ed.
New York: Springer-Verlag, pp. 50-65, 1990.
Nagell, T. ``Theory of Quadratic Residues.'' Ch. 4 in Introduction to Number Theory. New York: Wiley, 1951.
Riesel, H. ``The Law of Quadratic Reciprocity.'' Prime Numbers and Computer Methods for Factorization, 2nd ed.
Boston, MA: Birkhäuser, pp. 279-281, 1994.
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 42-49, 1993.