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 Exponential Difficulties 2 (Posted on 2004-11-27)
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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 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^á 3^â 5^è Then the three eqalities give

* á is odd, â and è are even

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

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

The smallest (á, â, è) 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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