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Commit0d74494

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‎main/algebra/fibonacci-numbers.html

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<ulclass="metadata page-metadata"data-bi-name="page info"lang="en-us"dir="ltr">
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Last update:
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<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April18, 202518:42:14">April18, 2025</span>&emsp;
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<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April22, 202501:19:59">April22, 2025</span>&emsp;
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<li>Cassini's identity:</li>
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</ul>
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<divclass="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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<ulclass="metadata page-metadata"data-bi-name="page info"lang="en-us"dir="ltr">
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<spanclass="contributors-text">Contributors:</span>
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<ulclass="contributors"data-bi-name="contributors"><li><ahref="https://github.com/gabrielsimoes"title="gabrielsimoes"data-bi-name="contributorprofile"target="_blank">gabrielsimoes</a> (24.64%)</li><li><ahref="https://github.com/jakobkogler"title="jakobkogler"data-bi-name="contributorprofile"target="_blank">jakobkogler</a> (21.43%)</li><li><ahref="#"title="Carlos Javier Blanco"data-bi-name="contributorprofile"target="_blank">Carlos Javier Blanco</a> (16.43%)</li><li><ahref="https://github.com/jxu"title="jxu"data-bi-name="contributorprofile"target="_blank">jxu</a> (15.36%)</li><li><ahref="https://github.com/madhur4127"title="madhur4127"data-bi-name="contributorprofile"target="_blank">madhur4127</a> (6.43%)</li><li><ahref="https://github.com/tcNickolas"title="tcNickolas"data-bi-name="contributorprofile"target="_blank">tcNickolas</a> (5.36%)</li><li><ahref="https://github.com/adamant-pwn"title="adamant-pwn"data-bi-name="contributorprofile"target="_blank">adamant-pwn</a> (2.5%)</li><li><ahref="https://github.com/Morass"title="Morass"data-bi-name="contributorprofile"target="_blank">Morass</a> (2.14%)</li><li><ahref="https://github.com/md-shamim-ahmad"title="md-shamim-ahmad"data-bi-name="contributorprofile"target="_blank">md-shamim-ahmad</a> (1.79%)</li><li><ahref="https://github.com/boxlesscat"title="boxlesscat"data-bi-name="contributorprofile"target="_blank">boxlesscat</a> (1.07%)</li><li><ahref="https://github.com/yeetholmes619"title="yeetholmes619"data-bi-name="contributorprofile"target="_blank">yeetholmes619</a> (1.07%)</li><li><ahref="https://github.com/pasthec"title="pasthec"data-bi-name="contributorprofile"target="_blank">pasthec</a> (0.71%)</li><li><ahref="https://github.com/mhayter"title="mhayter"data-bi-name="contributorprofile"target="_blank">mhayter</a> (0.36%)</li><li><ahref="https://github.com/conlacda"title="conlacda"data-bi-name="contributorprofile"target="_blank">conlacda</a> (0.36%)</li><li><ahref="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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