Mod[1, n] == n + 1 /; Element[-n, Integers] && -n > 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Mod", "[", RowBox[List["1", ",", "n"]], "]"]], "\[Equal]", RowBox[List["n", "+", "1"]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["-", "n"]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", "n"]], ">", "0"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <cn type='integer'> 1 </cn> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> &#10869; </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <rem /> <cn type='integer'> 1 </cn> <ci> $CellContext`n </ci> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List["1", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["n", "+", "1"]], "/;", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "n"]], ">", "0"]]]]]]]]]]

2001-10-29