JacobiSymbol
The Jacobi symbol (n/m), generalising the Legendre symbol to composite m.
Wikipedia
Jacobi symbolMathWorldJacobiSymbolWikidataQ241015Wolfram LanguageJacobiSymbol✓Rosetta CodeJacobi symbolJacobiSymbol(n, m)the Jacobi symbol Details
- Generalizes the Legendre symbol from prime
to any odd , by multiplying the Legendre symbols of 's prime factors. - 0 whenever
and share a factor. - Completely multiplicative in the top argument:
. - By convention
for every . - Unlike the Legendre symbol,
doesn't imply is a quadratic residue mod when is composite.
Examples
See also: PowerMod, LegendreSymbol, KroneckerSymbol