Fermat's Last Theorem/Cubic

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


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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

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3$
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