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<a accesskey="3" href="page.php?w=Euclid%27s_lemma&amp;p=2">3.Next</a>
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<p>In <a href="page.php?w=algebra">algebra</a> and <a href="page.php?w=number_theory">number theory</a>, <b>Euclid's lemma</b> is a <a href="page.php?w=lemma_%28mathematics%29">lemma</a> that captures a fundamental property of <a href="page.php?w=prime_number">prime number</a>s:For example, if , , , then , and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In fact, .</p>

<p>The lemma first appeared in <a href="page.php?w=Euclid">Euclid</a>'s <a href="page.php?w=Euclid%27s_Elements">Elements</a>,</p><p>
<a accesskey="3" href="page.php?w=Euclid%27s_lemma&amp;p=2">3.Next</a>
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