Let \(f(n)\) return the number of distinct ordered pairs of positive integers \((a,b)\) such that for each ordered pair, \(a^2+b^2=n\) . Note that when \(a \neq b, (a,b)\), and \((b,a)\) are distinct. What is the smallest positive integer \(n\) for which \(f(n)=3\) ?
Please write an approach to get to the answer.
The only way to do this is brute force.
The smallest n that works is 200: 200 = 2^2 + 14^2 = 10^2 + 10^2 = 14^2 + 2^2