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The Perfect Cube (Posted on 2003-08-12) Difficulty: 3 of 5
Can both n + 3 and n^2 + 3 be perfect cubes if n is an integer ?

See The Solution Submitted by Jayaram S    
Rating: 4.1667 (6 votes)

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re: My Idea | Comment 12 of 21 |
(In reply to My Idea by Ravi Raja)

Well, I tried n=4, and n+3 is 7, which isn't a perfect cube, so I think that it's impossible for n+3 to be a perfect cube.

.. You could prove that it's possible, of course, by finding a single example, but no number of counterexamples will ever serve as sufficient disproof.
  Posted by DJ on 2003-08-14 07:25:55

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