Squares which are Difference between Two Cubes

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Theorem

$169$ is the smallest square number which is the difference between two cubes:

$169 = 8^3 - 7^3$



Proof

\(\displaystyle 8^3 - 7^3\) \(=\) \(\displaystyle 512 - 343\)
\(\displaystyle \) \(=\) \(\displaystyle 169\)
\(\displaystyle \) \(=\) \(\displaystyle 13^2\)



Sources