Whose hypothesised that there was no natural solution to:

$\displaystyle

a^3 + b^3 = c^3 \hfill \\

$

$\displaystyle

a,b,c \in N \hfill \\

$

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- Feb 25th 2008, 06:26 PM #1

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- Feb 25th 2008, 06:30 PM #2

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Fermat. The proof is not easy. Probably the best way to prove this is to work in $\displaystyle \mathbb{Z}[\omega] = \{ a + b\omega|a,b\in \mathbb{Z} \}$ where $\displaystyle \omega = e^{2\pi i/3}$ called the Eisenstein integers. And even that proof is not so trivial.