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JacobiSymbol




Mathematica Notation

Traditional Notation









Number Theory Functions > JacobiSymbol[n,m] > Zeros





http://functions.wolfram.com/13.08.30.0001.01









  


  








Input Form





JacobiSymbol[n, p] == 0 /; Element[n/p, Integers] && Element[p, Primes] && p > 2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiSymbol", "[", RowBox[List["n", ",", "p"]], "]"]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[FractionBox["n", "p"], "\[Element]", "Integers"]], "\[And]", RowBox[List["p", "\[Element]", "Primes"]], "\[And]", RowBox[List["p", ">", "2"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mo> ( </mo> <mfrac> <mi> n </mi> <mi> p </mi> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;n&quot;, &quot;p&quot;], &quot;)&quot;]], JacobiSymbol, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mfrac> <mi> n </mi> <mi> p </mi> </mfrac> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &gt; </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiSymbol </ci> <ci> n </ci> <ci> p </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <ci> n </ci> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> <apply> <in /> <ci> p </ci> <primes /> </apply> <apply> <gt /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiSymbol", "[", RowBox[List["n_", ",", "p_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[FractionBox["n", "p"], "\[Element]", "Integers"]], "&&", RowBox[List["p", "\[Element]", "Primes"]], "&&", RowBox[List["p", ">", "2"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29