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 Documentation / Mathematica / Built-in Functions / Mathematical Functions / Number Theory  /
JacobiSymbol

  • JacobiSymbol[ n , m ] gives the Jacobi symbol .
  • Integer mathematical function (see Section A.3.10).
  • For prime , the Jacobi symbol reduces to the Legendre symbol. The Legendre symbol is equal to depending on whether is a quadratic residue modulo .
  • See the Mathematica book: Section 3.2.4.
  • See also: FactorInteger, MoebiusMu.

    Further Examples

    is not a quadraic residue modulo but is.

    In[1]:=

    Out[1]=

    Here is confirmation.

    In[2]:=

    Out[2]=