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http://functions.wolfram.com/13.10.32.0001.01
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Sum[Mod[Binomial[n, k], 2], {k, 0, n}] == 2^DigitCount[n, 2, 1]
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Cell[BoxData[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], RowBox[List["Mod", "[", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n", ",", "k"]], "]"]], ",", "2"]], "]"]]]], "\[Equal]", SuperscriptBox["2", RowBox[List["DigitCount", "[", RowBox[List["n", ",", "2", ",", "1"]], "]"]]]]]]]
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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> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <semantics> <mrow> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> n </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <ci> Binomial </ci> <ci> $CellContext`n </ci> <ci> FE`Conversion`Private`k </ci> </apply> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ⩵ </mo> <msup> <mn> 2 </mn> <mrow> <msubsup> <mi> s </mi> <mn> 2 </mn> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <rem /> <apply> <ci> Binomial </ci> <ci> $CellContext`n </ci> <ci> FE`Conversion`Private`k </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n_"], RowBox[List["Mod", "[", RowBox[List[RowBox[List["Binomial", "[", RowBox[List["n_", ",", "k"]], "]"]], ",", "2"]], "]"]]]], "]"]], "\[RuleDelayed]", SuperscriptBox["2", RowBox[List["DigitCount", "[", RowBox[List["n", ",", "2", ",", "1"]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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