Quadratic ResidueQuadratic Residue a prime number except 2If has an integer solution, is a quadratic residue of divisor and a quadratic nonresidue otherwise.Consider . is a quadratic residue![]() is a quadratic nonresidue![]() Legendre's symbols
If , then
![]() First supplementary law ![]() Second supplementary law ![]() Reciprocity law a prime number other than 2![]() Jacobi's symbols an odd number other than 1 (factorization into prime numbers)If , then![]()
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