JacobiSymbol[k n, m] == JacobiSymbol[k, m] JacobiSymbol[n, m] /; GCD[n, m] == 1 && GCD[n, k] == 1 && Element[(m - 3)/2, Integers] && (m - 3)/2 >= 0

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<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> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mi> m </mi> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, FractionBox[RowBox[List[&quot;k&quot;, &quot; &quot;, &quot;n&quot;]], &quot;m&quot;], &quot;)&quot;]], JacobiSymbol, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <semantics> <mrow> <mo> ( </mo> <mfrac> <mi> k </mi> <mi> m </mi> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;k&quot;, &quot;m&quot;], &quot;)&quot;]], JacobiSymbol, Rule[Editable, False]] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mfrac> <mi> n </mi> <mi> m </mi> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;n&quot;, &quot;m&quot;], &quot;)&quot;]], JacobiSymbol, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiSymbol </ci> <apply> <times /> <ci> k </ci> <ci> n </ci> </apply> <ci> m </ci> </apply> <apply> <times /> <apply> <ci> JacobiSymbol </ci> <ci> k </ci> <ci> m </ci> </apply> <apply> <ci> JacobiSymbol </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <gcd /> <ci> n </ci> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <gcd /> <ci> n </ci> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29