81 lines
5.1 KiB
HTML
81 lines
5.1 KiB
HTML
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<h2>Pythagorean Polygons</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 292</h3><span style="width:300px;color:#666;">Published on Saturday, 15th May 2010, 01:00 am; Solved by 392</span></div>
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<p>We shall define a <i>pythagorean polygon</i> to be a <b>convex polygon</b> with the following properties:<br />
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<ul>
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<li>there are at least three vertices,</li>
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<li>no three vertices are aligned,</li>
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<li>each vertex has <b>integer coordinates</b>,</li>
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<li>each edge has <b>integer length</b>.</li></ul></p>
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<p>For a given integer <var>n</var>, define P(<var>n</var>) as the number of distinct pythagorean polygons for which the perimeter is <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> <var>n</var>.<br />
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Pythagorean polygons should be considered distinct as long as none is a translation of another.</p>
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<p>You are given that P(4) = 1, P(30) = 3655 and P(60) = 891045.<br />
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Find P(120).</p>
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