Square which is 2 Less than Cube

Theorem

$25$ is the only square number which is $2$ less than a cube:

$5^2 + 2 = 3^3$


Proof


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Historical Note

The fact that $25$ is the only was stated without proof by Pierre de Fermat.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $25$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $25$
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