Problem:
For , let , where there are zeros between the 1 and the 6 . Let be the number of factors of 2 in the prime factorization of . What is the maximum value of
Answer Choices:
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B.
C.
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E.
Solution:
Note that . For , the first term is not divisible by , so . For , the first term is divisible by , but the second term is not, so . For , and because the second factor is even, . In fact the second factor is a sum of cubes so
The factor is divisible by 2 but not 4 , and the second factor is odd, so contributes one more factor of 2 . Hence the maximum value for is .
The problems on this page are the property of the MAA's American Mathematics Competitions