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Mod




Mathematica Notation

Traditional Notation









Integer Functions > Mod[m,n] > General characteristics > Symmetries and periodicities > Periodicity





http://functions.wolfram.com/04.06.04.0007.01









  


  








Input Form





Mod[m + k n, n] == Mod[m, n] /; Element[k, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Mod", "[", RowBox[List[RowBox[List["m", "+", RowBox[List["k", " ", "n"]]]], ",", "n"]], "]"]], "\[Equal]", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]








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> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <plus /> <ci> FE`Conversion`Private`m </ci> <apply> <times /> <ci> FE`Conversion`Private`k </ci> <ci> FE`Conversion`Private`n </ci> </apply> </apply> <ci> FE`Conversion`Private`n </ci> </apply> </annotation-xml> </semantics> <mo> &#10869; </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> FE`Conversion`Private`m </ci> <ci> FE`Conversion`Private`n </ci> </apply> </annotation-xml> </semantics> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <rem /> <apply> <plus /> <ci> FE`Conversion`Private`m </ci> <apply> <times /> <ci> FE`Conversion`Private`k </ci> <ci> FE`Conversion`Private`n </ci> </apply> </apply> <ci> FE`Conversion`Private`n </ci> </apply> <apply> <rem /> <ci> FE`Conversion`Private`m </ci> <ci> FE`Conversion`Private`n </ci> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List[RowBox[List["m_", "+", RowBox[List["k_", " ", "n_"]]]], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]


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





2007-05-02