HMMT 二月 2007 · GEN1 赛 · 第 5 题

英文解析

5. [ 4 ] Find the smallest positive integer that is twice a perfect square and three times a perfect cube.
   Answer: 648 . Let n be such a number. If n is divisible by 2 and 3 exactly e and e times, then
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   e is odd and a multiple of three, and e is even and one more than a multiple of three. The smallest
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   possible exponents are n = 3 and n = 4. The answer is then 2 · 3 = 648 .
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   n n