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Looking for n (Posted on 2004-02-24) Difficulty: 3 of 5
Let n be the smallest positive integer such that n(n+1)(n+2)(n+3) can be expressed as either a perfect square or a perfect cube (not necessarily both).

Find n, or prove that this is not possible.

See The Solution Submitted by Aaron    
Rating: 4.2857 (7 votes)

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Hints/Tips Not a square | Comment 1 of 12
Out of any four consecutive integers, one will be a multiple of 4, and other will be even, but not multiple of 4. Thus, the product of the four integers will be even, but NOT a multiple of four -- so it cannot be a square.
  Posted by Federico Kereki on 2004-02-24 15:20:46
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