Problem:
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than
Answer Choices:
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B.
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E.
Solution:
Since the integer is neither prime nor square, it is divisible either by two distinct primes or by the cube of a prime. The smallest prime numbers not less than are and . Since , the smallest number satisfying this description is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions