IMO 1983 LL CUB22

Does there exist an infinite number of sets C consisting of 1983

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IMO 1983 LL CUB22

Origin: CUB

Problem

Does there exist an infinite number of sets C consisting of 1983 consecutive natural numbers such that each of the numbers is divisible by some number of the form a1983, with a \inN, a ̸= 1?