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‎main/algebra/fibonacci-numbers.html

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<ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr">
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Last update:
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<span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date" title="April 18, 2025 18:42:14">April 18, 2025</span>&emsp;
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<span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date" title="April 22, 2025 01:19:59">April 22, 2025</span>&emsp;
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<li>Cassini's identity:</li>
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</ul>
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<div class="arithmatex">$$F_{n-1} F_{n+1} - F_n^2 = (-1)^n$$</div>
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<blockquote>
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<p>This can be proved by induction. A one-line proof by Knuth comes from taking the determinant of the 2x2 matrix form below.</p>
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</blockquote>
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<ul>
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<li>The "addition" rule:</li>
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<ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr">
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<span class="contributors-text">Contributors:</span>
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<ul class="contributors" data-bi-name="contributors"><li><a href="https://github.com/gabrielsimoes" title="gabrielsimoes" data-bi-name="contributorprofile" target="_blank">gabrielsimoes</a> (24.82%)</li><li><a href="https://github.com/jakobkogler" title="jakobkogler" data-bi-name="contributorprofile" target="_blank">jakobkogler</a> (21.58%)</li><li><a href="#" title="Carlos Javier Blanco" data-bi-name="contributorprofile" target="_blank">Carlos Javier Blanco</a> (16.55%)</li><li><a href="https://github.com/jxu" title="jxu" data-bi-name="contributorprofile" target="_blank">jxu</a> (15.11%)</li><li><a href="https://github.com/madhur4127" title="madhur4127" data-bi-name="contributorprofile" target="_blank">madhur4127</a> (6.47%)</li><li><a href="https://github.com/tcNickolas" title="tcNickolas" data-bi-name="contributorprofile" target="_blank">tcNickolas</a> (5.4%)</li><li><a href="https://github.com/adamant-pwn" title="adamant-pwn" data-bi-name="contributorprofile" target="_blank">adamant-pwn</a> (2.52%)</li><li><a href="https://github.com/Morass" title="Morass" data-bi-name="contributorprofile" target="_blank">Morass</a> (2.16%)</li><li><a href="https://github.com/md-shamim-ahmad" title="md-shamim-ahmad" data-bi-name="contributorprofile" target="_blank">md-shamim-ahmad</a> (1.8%)</li><li><a href="https://github.com/boxlesscat" title="boxlesscat" data-bi-name="contributorprofile" target="_blank">boxlesscat</a> (1.08%)</li><li><a href="https://github.com/yeetholmes619" title="yeetholmes619" data-bi-name="contributorprofile" target="_blank">yeetholmes619</a> (1.08%)</li><li><a href="https://github.com/pasthec" title="pasthec" data-bi-name="contributorprofile" target="_blank">pasthec</a> (0.72%)</li><li><a href="https://github.com/conlacda" title="conlacda" data-bi-name="contributorprofile" target="_blank">conlacda</a> (0.36%)</li><li><a href="https://github.com/ankit-kumar-dwivedi" title="ankit-kumar-dwivedi" data-bi-name="contributorprofile" target="_blank">ankit-kumar-dwivedi</a> (0.36%)</li></ul>
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<ul class="contributors" data-bi-name="contributors"><li><a href="https://github.com/gabrielsimoes" title="gabrielsimoes" data-bi-name="contributorprofile" target="_blank">gabrielsimoes</a> (24.64%)</li><li><a href="https://github.com/jakobkogler" title="jakobkogler" data-bi-name="contributorprofile" target="_blank">jakobkogler</a> (21.43%)</li><li><a href="#" title="Carlos Javier Blanco" data-bi-name="contributorprofile" target="_blank">Carlos Javier Blanco</a> (16.43%)</li><li><a href="https://github.com/jxu" title="jxu" data-bi-name="contributorprofile" target="_blank">jxu</a> (15.36%)</li><li><a href="https://github.com/madhur4127" title="madhur4127" data-bi-name="contributorprofile" target="_blank">madhur4127</a> (6.43%)</li><li><a href="https://github.com/tcNickolas" title="tcNickolas" data-bi-name="contributorprofile" target="_blank">tcNickolas</a> (5.36%)</li><li><a href="https://github.com/adamant-pwn" title="adamant-pwn" data-bi-name="contributorprofile" target="_blank">adamant-pwn</a> (2.5%)</li><li><a href="https://github.com/Morass" title="Morass" data-bi-name="contributorprofile" target="_blank">Morass</a> (2.14%)</li><li><a href="https://github.com/md-shamim-ahmad" title="md-shamim-ahmad" data-bi-name="contributorprofile" target="_blank">md-shamim-ahmad</a> (1.79%)</li><li><a href="https://github.com/boxlesscat" title="boxlesscat" data-bi-name="contributorprofile" target="_blank">boxlesscat</a> (1.07%)</li><li><a href="https://github.com/yeetholmes619" title="yeetholmes619" data-bi-name="contributorprofile" target="_blank">yeetholmes619</a> (1.07%)</li><li><a href="https://github.com/pasthec" title="pasthec" data-bi-name="contributorprofile" target="_blank">pasthec</a> (0.71%)</li><li><a href="https://github.com/mhayter" title="mhayter" data-bi-name="contributorprofile" target="_blank">mhayter</a> (0.36%)</li><li><a href="https://github.com/conlacda" title="conlacda" data-bi-name="contributorprofile" target="_blank">conlacda</a> (0.36%)</li><li><a href="https://github.com/ankit-kumar-dwivedi" title="ankit-kumar-dwivedi" data-bi-name="contributorprofile" target="_blank">ankit-kumar-dwivedi</a> (0.36%)</li></ul>
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