# Pythagorean Triplets

**Number Theory**Level 4

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 \(c\)?