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Posted on: July 25th, 2013 by

Suppose you arbitrarily select 101 numbers from 1,2,3,...200. Show that there exists 2 numbers among the 101 chosen numbers such that one number is divisible by the other.

via Moscow Math Olympiad

2 Responses to Divisibility

  1. Lizard had this to say about that:

    Group the 101 selected numbers by largest odd divisor. There are only 100 possible groups (1,3,5,...,199) so one group must have two elements. These two numbers' factorizations differ only by a power of two, so one divides the other.

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