In this chapter we describe a procedure for deciding efficiently whether or not the number a is a square modulo m. The main result, known as the law of quadratic reciprocity, was first proved by Gauss (1801) and is a cornerstone of number theory. The last section gives some applications of quadratic reciprocity to primality testing and testing for primitive roots.
KeywordsPrimitive Element Primitive Root Chinese Remainder Theorem Quadratic Residue Congruence Class
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