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EulerPhi




Mathematica Notation

Traditional Notation









Number Theory Functions > EulerPhi[n] > Inequalities





http://functions.wolfram.com/13.06.29.0004.01









  


  








Input Form





EulerPhi[n] >= Log[x n]/Log[x] /; n > 2 && Element[x, Reals] && x > 6








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EulerPhi", "[", "n", "]"]], "\[GreaterEqual]", FractionBox[RowBox[List["Log", "[", RowBox[List["x", " ", "n"]], "]"]], RowBox[List["Log", "[", "x", "]"]]]]], "/;", RowBox[List[RowBox[List["n", ">", "2"]], "\[And]", RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["x", ">", "6"]]]]]]]]








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> n </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mfrac> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &gt; </mo> <mn> 2 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> x </mi> <mo> &gt; </mo> <mn> 6 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <geq /> <apply> <ci> EulerPhi </ci> <ci> n </ci> </apply> <apply> <times /> <apply> <ln /> <apply> <times /> <ci> x </ci> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EulerPhi", "[", "n", "]"]], "\[GreaterEqual]", FractionBox[RowBox[List["Log", "[", RowBox[List["x", " ", "n"]], "]"]], RowBox[List["Log", "[", "x", "]"]]]]], "/;", RowBox[List[RowBox[List["n", ">", "2"]], "&&", RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", ">", "6"]]]]]]]]


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





2002-12-18