Math Help - a^3+b^3=c^3

1. a^3+b^3=c^3

Whose hypothesised that there was no natural solution to:

$

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

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

2. Originally Posted by Charbel
Whose hypothesised that there was no natural solution to:

$

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

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