ExtendedGCD[m, n] == {GCD[m, n], {r, s}}

Cell[BoxData[RowBox[List[RowBox[List["ExtendedGCD", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]], ",", RowBox[List["{", RowBox[List["r", ",", "s"]], "}"]]]], "}"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> egcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> m </mi> <mo> , </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mi> r </mi> <mo> , </mo> <mi> s </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> egcd </ci> <ci> m </ci> <ci> n </ci> </apply> <list> <apply> <gcd /> <ci> m </ci> <ci> n </ci> </apply> <list> <ci> r </ci> <ci> s </ci> </list> </list> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ExtendedGCD", "[", RowBox[List["m_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["GCD", "[", RowBox[List["m", ",", "n"]], "]"]], ",", RowBox[List["{", RowBox[List["r", ",", "s"]], "}"]]]], "}"]]]]]]

2001-10-29