|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/13.03.29.0004.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Prime[n] > (n m)/EulerPhi[m] - m^2/EulerPhi[m] /; n > 2 && m > 2
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Prime", "[", "n", "]"]], ">", RowBox[List[FractionBox[RowBox[List["n", " ", "m"]], RowBox[List["EulerPhi", "[", "m", "]"]]], "-", FractionBox[SuperscriptBox["m", "2"], RowBox[List["EulerPhi", "[", "m", "]"]]]]]]], "/;", RowBox[List[RowBox[List["n", ">", "2"]], "\[And]", RowBox[List["m", ">", "2"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> prime </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> > </mo> <mrow> <mfrac> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mrow> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mfrac> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mrow> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> > </mo> <mn> 2 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> > </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <gt /> <apply> <ci> prime </ci> <ci> n </ci> </apply> <apply> <plus /> <apply> <times /> <ci> n </ci> <ci> m </ci> <apply> <power /> <apply> <ci> EulerPhi </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> EulerPhi </ci> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Prime", "[", "n", "]"]], ">", RowBox[List[FractionBox[RowBox[List["n", " ", "m"]], RowBox[List["EulerPhi", "[", "m", "]"]]], "-", FractionBox[SuperscriptBox["m", "2"], RowBox[List["EulerPhi", "[", "m", "]"]]]]]]], "/;", RowBox[List[RowBox[List["n", ">", "2"]], "&&", RowBox[List["m", ">", "2"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|