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Exponential Difficulties 2 (Posted on 2004-11-27) Difficulty: 4 of 5
What's the least positive integer, n, having the following properties:
  • n = (a^2)/2
  • n = (b^3)/3
  • n = (c^5)/5
(where a, b, and c are integers)

See The Solution Submitted by SilverKnight    
Rating: 4.0000 (5 votes)

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Solution There's a better choice | Comment 8 of 9 |

As we want N to be as small as possible, we insist that it is composed of powers of 2, 3 and 5. (Other factors simply make N larger without helping to fulfill any of the constraints. We have

N = 2^ 3^ 5^ Then the three eqalities give

* is odd, and are even

* is one more than a multiple of 3, and are multiples of 3

* is one more than a multiple of 5, and are multiples of 5.

The smallest (, , ) fitting these conditions is (15,10,6). Hence

N = 2^15 * 3^10 * 5^6


  Posted by FrankM on 2008-01-16 00:28:47
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