Description: The Legendre symbol is completely multiplicative in its left argument. Generalization of theorem 9.9(a) in ApostolNT p. 188 (which assumes that A and B are odd positive integers). Together with lgsqr this implies that the product of two quadratic residues or nonresidues is a residue, and the product of a residue and a nonresidue is a nonresidue. (Contributed by Mario Carneiro, 4-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | lgsdir | |