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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