Perfect Cubes

 The Problem:

Can you find a whole number n, so that both n + 3 and n² + 3 are perfect cubes?

 e.g.                  If n = 24, n + 3 = 27, which is equal to 3³.

 However,        n² + 3 = 24² + 3 = 579, which is between 6³ and 7³, so is not a perfect cube.

 If you can’t find a suitable value of n, can you prove that it’s an impossible search?

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Last modified: June 18, 2007