The number 1440000 satisfies the following equation:

$$1440000^3 - 1 = 1439940^3 + 71999^3 = 1440060^3 - 72001^3$$

By Fermat's Last Theorem (for which the case $n=3$ was proven by Euler), $1440000^3$ cannot be the sum or difference of 2 positive integer cubes. The above equation shows that $1440000^3-1$ is the sum and the difference of 2 positive integer cubes.

## Friday, January 20, 2017

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