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<p>equation  has no non-trivial (i.e. ) solutions in integers. In fact, it has none in <a href="page.php?w=Eisenstein_integers">Eisenstein integers</a>.</p>

<p>Both of these statements are also true for the equation .</p>

<p><big>Sum of first n cubes</big></p>
<p>The sum of the first  cubes is the th <a href="page.php?w=triangle_number">triangle number</a> squared:</p>

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:</p>

<p><b>Proofs.</b> gives a particularly simple derivation, by expanding each cube in the sum into a set of consecutive odd numbers. He begins by giving the identity</p>

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