Squares which are 4 Less than Cubes

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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


Historical Note

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


Sources