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diophantine abc = 2(a + b + c) with 0<a <=b <=c

Source: Dutch NMO 2014 p1

September 7, 2019
Diophantine equationdiophantinenumber theory

Problem Statement

Determine all triples (a,b,c)(a,b,c), where a,ba, b, and cc are positive integers that satisfy
a≤b≤ca \le b \le c and abc=2(a+b+c)abc = 2(a + b + c).
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