MathDB

7

Part of 1988 ITAMO

Problems(1)

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

Source: ITAMO 1998 p7

2/2/2020
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.
number theorygreatest common divisor