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The Legendre symbol's glyph extended to composite denominators.
Also known as: Generalised Legendre symbol, Kronecker symbol, Jacobi residue symbol
The Jacobi symbol looks identical to the Legendre symbol and generalises it to odd composite lower arguments, where it loses a property: a Jacobi symbol of 1 does not prove the top number is a square. That one-way failure is what primality tests exploit.
Denotes the product of Legendre symbols over the prime factorisation of an odd composite lower argument.
Contexts: Mathematics
Does not detect quadratic residues for composite moduli: a value of 1 is necessary but not sufficient, unlike the Legendre case.
Contexts: Mathematics
Is computable without factorising the modulus, which is what makes it usable in the Solovay–Strassen primality test.
Contexts: Mathematics
Two numerals set one above the other inside a tall pair of curved brackets, with no horizontal rule between them.