Fermat's Last Theorem/Cubic

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Theorem

The Diophantine equation $a^3 + b^3 = c^3$ has no solutions in strictly positive integers.


This is a special case of Fermat's Last Theorem.


Proof




Historical Note

The special case of Fermat's Last Theorem:

$\forall a, b, c \in \Z_{>0}$, the equation $a^3 + b^3 = c^3$ has no solutions

was proven by Leonhard Paul Euler.


Sources