Prove, a^2+b^2=c^2,there exists only 1 case such that a,b,c are consecutive non negative integers(3,4,5)
$n^2 + (n + 1)^2 = (n + 2)^2 \Rightarrow n^2 + n^2 + 2n + 1 = n^2 + 4n + 4 \Rightarrow 2n^2 2n + 1 = n^2 + 4n + 4 \Rightarrow n^2 - 2n - 3 = 0 \Rightarrow n = -1, 3$

Therefore, 3 is the only plausible solution.