CarmichaelLambda[2^n] == EulerPhi[2^n] /; 0 <= n <= 2

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["CarmichaelLambda", "[", SuperscriptBox["2", "n"], "]"]], "\[Equal]", RowBox[List["EulerPhi", "[", SuperscriptBox["2", "n"], "]"]]]], "/;", RowBox[List["0", "\[LessEqual]", "n", "\[LessEqual]", "2"]]]]]]

<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> &#955; </mi> <annotation-xml encoding='MathML-Content'> <ci> CarmichaelLambda </ci> </annotation-xml> </semantics> <mo> ( </mo> <msup> <mn> 2 </mn> <mi> n </mi> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <msup> <mn> 2 </mn> <mi> n </mi> </msup> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 0 </mn> <mo> &#8804; </mo> <mi> n </mi> <mo> &#8804; </mo> <mn> 2 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> CarmichaelLambda </ci> <apply> <power /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> <apply> <ci> EulerPhi </ci> <apply> <power /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <leq /> <cn type='integer'> 0 </cn> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["CarmichaelLambda", "[", SuperscriptBox["2", "n_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["EulerPhi", "[", SuperscriptBox["2", "n"], "]"]], "/;", RowBox[List["0", "\[LessEqual]", "n", "\[LessEqual]", "2"]]]]]]]]

2001-10-29