# Proofathon Squares!

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.

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