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May 23, 2013 at 21:31 comment added whuber The equation is a cubic (parameterized by $n$), so it's possible a more efficient method to obtain all solutions can be found by computing generators of its group of integral points. But typically these groups are so small--I haven't found one larger than $12$ yet--as a practical matter it might not be worth the effort.
May 23, 2013 at 21:12 history edited whuber CC BY-SA 3.0
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May 23, 2013 at 21:01 history edited whuber CC BY-SA 3.0
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May 23, 2013 at 20:51 comment added RunnyKine I appreciate the explanation in this answer. +1
May 23, 2013 at 20:41 comment added whuber You're welcome. You shouldn't be so quick to accept this answer, though: this community does a great job of improving answers over the course of a day or two. Much better answers might appear soon :-).
May 23, 2013 at 20:40 history edited whuber CC BY-SA 3.0
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May 23, 2013 at 20:17 comment added Moderat This is fantastic thanks very much whuber
May 23, 2013 at 20:17 vote accept Moderat
May 23, 2013 at 19:55 history answered whuber CC BY-SA 3.0