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	<id>https://www.ellipticcurve.info/Pascal%E2%80%99s_triangle/history?feed=atom</id>
	<title>Pascal’s triangle - Revision history</title>
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	<updated>2026-05-06T20:13:57Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.42.3</generator>
	<entry>
		<id>https://www.ellipticcurve.info/index.php?title=Pascal%E2%80%99s_triangle&amp;diff=100&amp;oldid=prev</id>
		<title>Rational Point: /* Notation */ off by one?</title>
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		<updated>2024-12-28T03:22:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Notation: &lt;/span&gt; off by one?&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 03:22, 28 December 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l25&quot;&gt;Line 25:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 25:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Notation ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Notation ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;n \choose k&amp;lt;/math&amp;gt; is the mathematical symbol for the &#039;&#039;k&#039;&#039;&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; entry of the &#039;&#039;n&#039;&#039;&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; row of &#039;&#039;&#039;Pascal’s triangle&#039;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;n \choose k&amp;lt;/math&amp;gt; is the mathematical symbol for the &#039;&#039;k&#039;&#039;&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; entry of the &#039;&#039;n&#039;&#039;&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; row of &#039;&#039;&#039;Pascal’s triangle&#039;&#039;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, (counting from zero!)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;{n\choose k} = \frac{n!}{k!(n-k)!}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;{n\choose k} = \frac{n!}{k!(n-k)!}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;{n\choose k} = {n-1\choose k-1}+{n-1\choose k}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;:&amp;lt;math&amp;gt;{n\choose k} = {n-1\choose k-1}+{n-1\choose k}&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rational Point</name></author>
	</entry>
	<entry>
		<id>https://www.ellipticcurve.info/index.php?title=Pascal%E2%80%99s_triangle&amp;diff=99&amp;oldid=prev</id>
		<title>Rational Point: /_\</title>
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		<updated>2024-12-27T23:26:31Z</updated>

		<summary type="html">&lt;p&gt;/_\&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{|style=&amp;quot;text-align:center;&lt;br /&gt;
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== Notation ==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;n \choose k&amp;lt;/math&amp;gt; is the mathematical symbol for the &amp;#039;&amp;#039;k&amp;#039;&amp;#039;&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; entry of the &amp;#039;&amp;#039;n&amp;#039;&amp;#039;&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; row of &amp;#039;&amp;#039;&amp;#039;Pascal’s triangle&amp;#039;&amp;#039;&amp;#039;.&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;{n\choose k} = \frac{n!}{k!(n-k)!}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;{n\choose k} = {n-1\choose k-1}+{n-1\choose k}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>Rational Point</name></author>
	</entry>
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