GCD[Mod[n, m], m] == GCD[n, m] /; m > 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["GCD", "[", RowBox[List[RowBox[List["Mod", "[", RowBox[List["n", ",", "m"]], "]"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["GCD", "[", RowBox[List["n", ",", "m"]], "]"]]]], "/;", RowBox[List["m", ">", "0"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> m </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`n </ci> <ci> $CellContext`m </ci> </apply> </annotation-xml> </semantics> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> gcd </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <gcd /> <apply> <rem /> <ci> $CellContext`n </ci> <ci> $CellContext`m </ci> </apply> <ci> m </ci> </apply> <apply> <gcd /> <ci> n </ci> <ci> m </ci> </apply> </apply> <apply> <gt /> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GCD", "[", RowBox[List[RowBox[List["Mod", "[", RowBox[List["n_", ",", "m_"]], "]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["GCD", "[", RowBox[List["n", ",", "m"]], "]"]], "/;", RowBox[List["m", ">", "0"]]]]]]]]

2001-10-29