Problem

Source: ELMO Shortlist 2013: Problem N1, by Matthew Babbitt

Tags: parameterization, number theory, easy problem.



Find all ordered triples of non-negative integers $(a,b,c)$ such that $a^2+2b+c$, $b^2+2c+a$, and $c^2+2a+b$ are all perfect squares. Proposed by Matthew Babbitt