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problem 75 · 14 lines

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<p>It turns out that $\pu{12 cm}$ is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples.</p>
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<li>$\pu{\mathbf{12} \mathbf{cm}}$: $(3,4,5)$</li>
<li>$\pu{\mathbf{24} \mathbf{cm}}$: $(6,8,10)$</li>
<li>$\pu{\mathbf{30} \mathbf{cm}}$: $(5,12,13)$</li>
<li>$\pu{\mathbf{36} \mathbf{cm}}$: $(9,12,15)$</li>
<li>$\pu{\mathbf{40} \mathbf{cm}}$: $(8,15,17)$</li>
<li>$\pu{\mathbf{48} \mathbf{cm}}$: $(12,16,20)$</li></ul>
<p>In contrast, some lengths of wire, like $\pu{20 cm}$, cannot be bent to form an integer sided right angle triangle, and other lengths allow more than one solution to be found; for example, using $\pu{120 cm}$ it is possible to form exactly three different integer sided right angle triangles.</p>
<ul style="list-style-type:none;">
<li>$\pu{\mathbf{120} \mathbf{cm}}$: $(30,40,50)$, $(20,48,52)$, $(24,45,51)$</li></ul>
<p>Given that $L$ is the length of the wire, for how many values of $L \le 1\,500\,000$ can exactly one integer sided right angle triangle be formed?</p>
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