Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File


Developed with Mathematica -- Download a Free Trial Version

variants of this functions

Mathematica Notation

Traditional Notation

Integer Functions > Fibonacci[nu] > Identities > Functional identities > Relations of special kind




Input Form

Fibonacci[GCD[m, n]] == GCD[Fibonacci[m], Fibonacci[n]] /; Element[m, Integers] && Element[n, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]], "]"]], "\[Equal]", RowBox[List["GCD", "[", RowBox[List[RowBox[List["Fibonacci", "[", "m", "]"]], ",", RowBox[List["Fibonacci", "[", "n", "]"]]]], "]"]]]], "/;", " ", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[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> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> </msub> <mo> &#10869; </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mi> m </mi> </msub> <mo> , </mo> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mi> n </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Fibonacci </ci> <apply> <gcd /> <ci> m </ci> <ci> n </ci> </apply> </apply> <apply> <gcd /> <apply> <ci> Fibonacci </ci> <ci> m </ci> </apply> <apply> <ci> Fibonacci </ci> <ci> n </ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", RowBox[List["GCD", "[", RowBox[List["m_", ",", "n_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["GCD", "[", RowBox[List[RowBox[List["Fibonacci", "[", "m", "]"]], ",", RowBox[List["Fibonacci", "[", "n", "]"]]]], "]"]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]]]

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