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MMO 137 Moscow MO 1947 101 no from set 1, ...,200, pair divides another

Source:

July 20, 2019
number theorydivisiblecombinatorics

Problem Statement

a) 101101 numbers are selected from the set 1,2,...,2001, 2, . . . , 200. Prove that among the numbers selected there is a pair in which one number is divisible by the other.
b) One number less than 1616, and 9999 other numbers are selected from the set 1,2,...,2001, 2, . . . , 200. Prove that among the selected numbers there are two such that one divides the other.
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