# Pythagorean Triplets

Given that positive integers $$a,b$$ and $$c$$ satisfy the equation $$a^2 + b^2=c^2$$ with $$a,b$$ consecutive, and we know that $$(a,b,c) = (3,4,5), (20,21,29)$$ are two smallest possible solutions satisfying this constraint such that $$c$$ is minimized. What is the third smallest value of $$c$$?

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