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max of gcd(a, b) + gcd(b, c) + gcd(c, a) when a + b + c = 5n.

Source: Dutch IMO TST1 2019 p3

January 10, 2020
maximumGCDgreatest common divisornumber theory

Problem Statement

Let nn be a positive integer. Determine the maximum value of gcd(a,b)+gcd(b,c)+gcd(c,a)gcd(a, b) + gcd(b, c) + gcd(c, a) for positive integers a,b,ca, b, c such that a+b+c=5na + b + c = 5n.
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