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 canít find a suitable value of n, can you prove that itís an impossible search?

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Last modified: June 18, 2007