# Squares which are 4 Less than Cubes

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## Contents

## 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

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