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@@ -3705,8 +3705,8 @@ n = 3 a + b
<h3 id="3">3. &nbsp; 正确性证明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>使用反证法，只分析 <span class="arithmatex">\(n \geq 3\)</span> 的情况。</p>
<ol>
<li><strong>所有因子 <span class="arithmatex">\(\leq 3\)</span></strong> :假设最优切分方案中存在 <span class="arithmatex">\(\geq 4\)</span> 的因子 <span class="arithmatex">\(x\)</span> ，那么一定可以将其继续划分为 <span class="arithmatex">\(2(x-2)\)</span> ，从而获得更大的乘积。这与假设矛盾。</li>
<li><strong>切分方案不包含 <span class="arithmatex">\(1\)</span></strong> :假设最优切分方案中存在一个因子 <span class="arithmatex">\(1\)</span> ，那么它一定可以合并入另外一个因子中，以获取更大乘积。这与假设矛盾。</li>
<li><strong>所有因子 <span class="arithmatex">\(\leq 3\)</span></strong> ：假设最优切分方案中存在 <span class="arithmatex">\(\geq 4\)</span> 的因子 <span class="arithmatex">\(x\)</span> ，那么一定可以将其继续划分为 <span class="arithmatex">\(2(x-2)\)</span> ，从而获得更大的乘积。这与假设矛盾。</li>
<li><strong>切分方案不包含 <span class="arithmatex">\(1\)</span></strong> ：假设最优切分方案中存在一个因子 <span class="arithmatex">\(1\)</span> ，那么它一定可以合并入另外一个因子中，以获取更大乘积。这与假设矛盾。</li>
<li><strong>切分方案最多包含两个 <span class="arithmatex">\(2\)</span></strong> ：假设最优切分方案中包含三个 <span class="arithmatex">\(2\)</span> ，那么一定可以替换为两个 <span class="arithmatex">\(3\)</span> ，乘积更大。这与假设矛盾。</li>
</ol>