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3 of n positive integers with same gcd, have also the same gcd

Source: ITAMO 1998 p7

February 2, 2020
number theorygreatest common divisor

Problem Statement

Given n≥3n \ge 3 positive integers not exceeding 100100, let dd be their greatest common divisor. Show that there exist three of these numbers whose greatest common divisor is also equal to dd.
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