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6784 | 6794 | <ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr"> |
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6786 | 6796 | Last update: |
6787 | | - <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date" title="August 15, 2025 21:04:35 UTC">August 15, 2025</span>  |
| 6797 | + <span class="git-revision-date-localized-plugin git-revision-date-localized-plugin-date" title="October 29, 2025 17:22:34 UTC">October 29, 2025</span>  |
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@@ -6822,7 +6832,7 @@ <h1 id="linear-diophantine-equation">Linear Diophantine Equation<a class="header |
6822 | 6832 | <li>finding a solution with minimum value of <span class="arithmatex">$x + y$</span></li> |
6823 | 6833 | </ul> |
6824 | 6834 | <h2 id="the-degenerate-case">The degenerate case<a class="headerlink" href="#the-degenerate-case" title="Permanent link">¶</a></h2> |
6825 | | -<p>A degenerate case that need to be taken care of is when <span class="arithmatex">$a = b = 0$</span>. It is easy to see that we either have no solutions or infinitely many solutions, depending on whether <span class="arithmatex">$c = 0$</span> or not. In the rest of this article, we will ignore this case.</p> |
| 6835 | +<p>A degenerate case that needs to be taken care of is when <span class="arithmatex">$a = b = 0$</span>. It is easy to see that we either have no solutions or infinitely many solutions, depending on whether <span class="arithmatex">$c = 0$</span> or not. In the rest of this article, we will ignore this case.</p> |
6826 | 6836 | <h2 id="analytic-solution">Analytic solution<a class="headerlink" href="#analytic-solution" title="Permanent link">¶</a></h2> |
6827 | 6837 | <p>When <span class="arithmatex">$a \neq 0$</span> and <span class="arithmatex">$b \neq 0$</span>, the equation <span class="arithmatex">$ax+by=c$</span> can be equivalently treated as either of the following:</p> |
6828 | 6838 | <div class="arithmatex">$$\begin{align} |
@@ -6975,7 +6985,7 @@ <h2 id="practice-problems">Practice Problems<a class="headerlink" href="#practic |
6975 | 6985 |
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6976 | 6986 | <ul class="metadata page-metadata" data-bi-name="page info" lang="en-us" dir="ltr"> |
6977 | 6987 | <span class="contributors-text">Contributors:</span> |
6978 | | - <ul class="contributors" data-bi-name="contributors"><li><a href="https://github.com/thanhtnguyen" title="thanhtnguyen" data-bi-name="contributorprofile" target="_blank">thanhtnguyen</a> (57.64%)</li><li><a href="https://github.com/jakobkogler" title="jakobkogler" data-bi-name="contributorprofile" target="_blank">jakobkogler</a> (17.47%)</li><li><a href="https://github.com/adamant-pwn" title="adamant-pwn" data-bi-name="contributorprofile" target="_blank">adamant-pwn</a> (12.67%)</li><li><a href="https://github.com/jxu" title="jxu" data-bi-name="contributorprofile" target="_blank">jxu</a> (4.8%)</li><li><a href="https://github.com/tcNickolas" title="tcNickolas" data-bi-name="contributorprofile" target="_blank">tcNickolas</a> (3.06%)</li><li><a href="https://github.com/likecs" title="likecs" data-bi-name="contributorprofile" target="_blank">likecs</a> (2.18%)</li><li><a href="https://github.com/boxlesscat" title="boxlesscat" data-bi-name="contributorprofile" target="_blank">boxlesscat</a> (1.31%)</li><li><a href="https://github.com/arjunUpatel" title="arjunUpatel" data-bi-name="contributorprofile" target="_blank">arjunUpatel</a> (0.44%)</li><li><a href="https://github.com/traxex2" title="traxex2" data-bi-name="contributorprofile" target="_blank">traxex2</a> (0.44%)</li></ul> |
| 6988 | + <ul class="contributors" data-bi-name="contributors"><li><a href="https://github.com/thanhtnguyen" title="thanhtnguyen" data-bi-name="contributorprofile" target="_blank">thanhtnguyen</a> (57.64%)</li><li><a href="https://github.com/jakobkogler" title="jakobkogler" data-bi-name="contributorprofile" target="_blank">jakobkogler</a> (17.47%)</li><li><a href="https://github.com/adamant-pwn" title="adamant-pwn" data-bi-name="contributorprofile" target="_blank">adamant-pwn</a> (12.67%)</li><li><a href="https://github.com/jxu" title="jxu" data-bi-name="contributorprofile" target="_blank">jxu</a> (4.8%)</li><li><a href="https://github.com/tcNickolas" title="tcNickolas" data-bi-name="contributorprofile" target="_blank">tcNickolas</a> (2.62%)</li><li><a href="https://github.com/likecs" title="likecs" data-bi-name="contributorprofile" target="_blank">likecs</a> (2.18%)</li><li><a href="https://github.com/boxlesscat" title="boxlesscat" data-bi-name="contributorprofile" target="_blank">boxlesscat</a> (1.31%)</li><li><a href="https://github.com/Kyaki101" title="Kyaki101" data-bi-name="contributorprofile" target="_blank">Kyaki101</a> (0.44%)</li><li><a href="https://github.com/arjunUpatel" title="arjunUpatel" data-bi-name="contributorprofile" target="_blank">arjunUpatel</a> (0.44%)</li><li><a href="https://github.com/traxex2" title="traxex2" data-bi-name="contributorprofile" target="_blank">traxex2</a> (0.44%)</li></ul> |
6979 | 6989 | </ul> |
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6981 | 6991 | </article> |
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