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6762 | 6772 | <ulclass="metadata page-metadata"data-bi-name="page info"lang="en-us"dir="ltr">
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6763 | 6773 |
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6764 | 6774 | Last update:
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6765 |
| -<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April18, 202518:42:14">April18, 2025</span>  |
| 6775 | +<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April22, 202501:19:59">April22, 2025</span>  |
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6767 | 6777 | <!-- Tags -->
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@@ -6799,6 +6809,9 @@ <h2 id="properties">Properties<a class="headerlink" href="#properties" title="Pe
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6799 | 6809 | <li>Cassini's identity:</li>
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6800 | 6810 | </ul>
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6801 | 6811 | <divclass="arithmatex">$$F_{n-1} F_{n+1} - F_n^2 = (-1)^n$$</div>
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| 6812 | +<blockquote> |
| 6813 | +<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> |
| 6814 | +</blockquote> |
6802 | 6815 | <ul>
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6803 | 6816 | <li>The "addition" rule:</li>
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6804 | 6817 | </ul>
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@@ -7021,7 +7034,7 @@ <h2 id="practice-problems">Practice Problems<a class="headerlink" href="#practic
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7021 | 7034 |
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7022 | 7035 | <ulclass="metadata page-metadata"data-bi-name="page info"lang="en-us"dir="ltr">
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7023 | 7036 | <spanclass="contributors-text">Contributors:</span>
|
7024 |
| -<ulclass="contributors"data-bi-name="contributors"><li><ahref="https://github.com/gabrielsimoes"title="gabrielsimoes"data-bi-name="contributorprofile"target="_blank">gabrielsimoes</a> (24.82%)</li><li><ahref="https://github.com/jakobkogler"title="jakobkogler"data-bi-name="contributorprofile"target="_blank">jakobkogler</a> (21.58%)</li><li><ahref="#"title="Carlos Javier Blanco"data-bi-name="contributorprofile"target="_blank">Carlos Javier Blanco</a> (16.55%)</li><li><ahref="https://github.com/jxu"title="jxu"data-bi-name="contributorprofile"target="_blank">jxu</a> (15.11%)</li><li><ahref="https://github.com/madhur4127"title="madhur4127"data-bi-name="contributorprofile"target="_blank">madhur4127</a> (6.47%)</li><li><ahref="https://github.com/tcNickolas"title="tcNickolas"data-bi-name="contributorprofile"target="_blank">tcNickolas</a> (5.4%)</li><li><ahref="https://github.com/adamant-pwn"title="adamant-pwn"data-bi-name="contributorprofile"target="_blank">adamant-pwn</a> (2.52%)</li><li><ahref="https://github.com/Morass"title="Morass"data-bi-name="contributorprofile"target="_blank">Morass</a> (2.16%)</li><li><ahref="https://github.com/md-shamim-ahmad"title="md-shamim-ahmad"data-bi-name="contributorprofile"target="_blank">md-shamim-ahmad</a> (1.8%)</li><li><ahref="https://github.com/boxlesscat"title="boxlesscat"data-bi-name="contributorprofile"target="_blank">boxlesscat</a> (1.08%)</li><li><ahref="https://github.com/yeetholmes619"title="yeetholmes619"data-bi-name="contributorprofile"target="_blank">yeetholmes619</a> (1.08%)</li><li><ahref="https://github.com/pasthec"title="pasthec"data-bi-name="contributorprofile"target="_blank">pasthec</a> (0.72%)</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> |
| 7037 | +<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> |
7025 | 7038 | </ul>
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7026 | 7039 |
|
7027 | 7040 | </article>
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