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JacobiSymbol

The Jacobi symbol (n/m), generalising the Legendre symbol to composite m.

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JacobiSymbol(n, m)the Jacobi symbol .

Domain: Number theory

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