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Also called the Aureum Theorema (Golden Theorem) by Gauß. If
and
are distinct
Odd Primes, then the Congruences
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|
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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.