ExtendedGCD[Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, p]] == {Abs[Subscript[n, 1]], {Subscript[m, 1], Subscript[m, 2], \[Ellipsis], Subscript[m, p - 1], Sign[Subscript[n, 1]]}} /; Subscript[n, 1] == Subscript[n, 2] == \[Ellipsis] == Subscript[n, p] && Subscript[m, 1] == Subscript[m, 2] == \[Ellipsis] == Subscript[m, p - 1] == 0

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> egcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> n </mi> <mi> p </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> m </mi> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> n </mi> <mi> p </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> m </mi> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> egcd </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> p </ci> </apply> </apply> <list> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <list> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Sign </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </list> </list> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> p </ci> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExtendedGCD", "[", RowBox[List[SubscriptBox["n_", "1"], ",", SubscriptBox["n_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["n_", "p_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["Abs", "[", SubscriptBox["nn", "1"], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["m", "1"], ",", SubscriptBox["m", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["m", RowBox[List["p", "-", "1"]]], ",", RowBox[List["Sign", "[", SubscriptBox["nn", "1"], "]"]]]], "}"]]]], "}"]], "/;", RowBox[List[RowBox[List[SubscriptBox["nn", "1"], "\[Equal]", SubscriptBox["n", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["n", "p"]]], "&&", RowBox[List[SubscriptBox["m", "1"], "\[Equal]", SubscriptBox["m", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["m", RowBox[List["p", "-", "1"]]], "\[Equal]", "0"]]]]]]]]]]

2007-05-02