Number of unrestricted partitions of an integer: Other identities (formula 04.16.32.0002)

PartitionsP

$Mathematica Notation$

Integer Functions

PartitionsP[n]

Other identities

Congruence properties

http://functions.wolfram.com/04.16.32.0002.01

Input Form

Mod[PartitionsP[7 n + 5], 7] == 0

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Mod", "[", RowBox[List[RowBox[List["PartitionsP", "[", RowBox[List[RowBox[List["7", "n"]], "+", "5"]], "]"]], ",", "7"]], "]"]], "\[Equal]", "0"]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 7 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <ci> PartitionsP </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`n </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> 7 </cn> </apply> </annotation-xml> </semantics> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <rem /> <apply> <ci> PartitionsP </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`n </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> 7 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List[RowBox[List["PartitionsP", "[", RowBox[List[RowBox[List["7", " ", "n_"]], "+", "5"]], "]"]], ",", "7"]], "]"]], "]"]], "\[RuleDelayed]", "0"]]]]

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

2001-10-29