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

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



Sources