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Multiplying gets a square? (Posted on 2004-06-26) Difficulty: 3 of 5
Is it possible to get a perfect square if you multiply three consecutive natural numbers?

See The Solution Submitted by Federico Kereki    
Rating: 3.0000 (5 votes)

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Solution Solution | Comment 24 of 25 |

Yes

As there is debate as to whether 0 (zero) is a member of the set of natural numbers or not, by asking "is it possible", it must be permitted to allow the acceptance of the more liberal definition. 
In addition, as it can also be defined that 0 can be a perfect square (02 = 0), we can see that 0 x 1 x 2 = 02; and, since 0, 1, and 2 are three consecutive natural numbers, the answer is yes.

Edited on July 26, 2008, 11:41 pm
  Posted by Dej Mar on 2008-07-26 06:21:09

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