1984 AHSME Problems/Problem 3
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Problem
Let be the smallest nonprime integer greater than with no prime factor less than . Then
Solution
Since the number isn't prime, it is a product of two primes. If the least integer were a product of more than two primes, then one prime could be removed without making the number prime or introducing any prime factors less than . These prime factors must be greater than , so the least prime factor is . Therefore, the least integer is , which is in .
See Also
1984 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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