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1986 USAMO Problem #1

Source:

August 16, 2011
AMCUSA(J)MOUSAMOinequalitiesblogsnumber theory unsolvednumber theory

Problem Statement

(a)(\text{a}) Do there exist 14 consecutive positive integers each of which is divisible by one or more primes pp from the interval 2≤p≤112\le p \le 11?
(b)(\text{b}) Do there exist 21 consecutive positive integers each of which is divisible by one or more primes pp from the interval 2≤p≤132\le p \le 13?
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