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EulerPhi




Mathematica Notation

Traditional Notation









Number Theory Functions > EulerPhi[n] > Inequalities





http://functions.wolfram.com/13.06.29.0007.01









  


  








Input Form





EulerPhi[m] EulerPhi[n] <= EulerPhi[m n] <= n EulerPhi[m]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EulerPhi", "[", "m", "]"]], RowBox[List["EulerPhi", "[", "n", "]"]]]], "\[LessEqual]", RowBox[List["EulerPhi", "[", RowBox[List["m", " ", "n"]], "]"]], "\[LessEqual]", RowBox[List["n", " ", RowBox[List["EulerPhi", "[", "m", "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8804; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <leq /> <apply> <times /> <apply> <ci> EulerPhi </ci> <ci> m </ci> </apply> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> </apply> <apply> <ci> EulerPhi </ci> <apply> <times /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> EulerPhi </ci> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EulerPhi", "[", "m", "]"]], " ", RowBox[List["EulerPhi", "[", "n", "]"]]]], "\[LessEqual]", RowBox[List["EulerPhi", "[", RowBox[List["m", " ", "n"]], "]"]], "\[LessEqual]", RowBox[List["n", " ", RowBox[List["EulerPhi", "[", "m", "]"]]]]]]]]


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





2002-12-18