Proofathon Squares!Number Theory Level 5
Let \(a\), \(b\) and \(c\) be positive integers that are less than \(1215\).Find the number of ordered triples \((a, b, c)\) such that \(a^2+7b^2+5\), \(b^2+7c^2+5\) and \(c^2+7a^2+5\) are all perfect squares.
This problem is from the Proofathon Number Theory Contest.
This problem is from the set "Olympiads and Contests Around the World -3". You can see the rest of the problems here.