Squares which are 4 Less than Cubes

Theorem

The only two square numbers which are $4$ less than a cube are:

$2^2 + 4 = 2^3$
$11^2 + 4 = 5^3$


Proof


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Historical Note

Pierre de Fermat correctly conjectured that there are only two square numbers which are $4$ less than a cube.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $121$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $121$
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