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
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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): $3$