Problem:
The least positive integer with exactly distinct positive divisors can be written in the form , where and are integers and is not a divisor of . What is ?
Answer Choices:
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Solution:
Let this positive integer be written as . The number of factors of this number is therefore . and this must equal . The prime factorization of 2021 is , so and . To minimize the integer, we set and . Then the integer is . Now and so m+k = 16+42 = \boxed
The problems on this page are the property of the MAA's American Mathematics Competitions