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Problem 1 -- Groovy GCDs

Source: 46th Austrian Mathematical Olympiad Regional Competition Problem 1

July 14, 2018
Austrianumber theoryGCD

Problem Statement

Determine all triples (a,b,c)(a,b,c) of positive integers satisfying the conditions
gcd⁡(a,20)=b\gcd(a,20) = b gcd⁡(b,15)=c\gcd(b,15) = c gcd⁡(a,c)=5\gcd(a,c) = 5
(Richard Henner)
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