Problem
ALG-B1-M12-P012 Variant 3, Problem 4
#12
★★★☆☆ Level 3 of 5
\(f:\mathbb Z\to\mathbb Z\), \(f(m+n)=f(m)+f(n)+mn\), \(f(1)=1\). Find \(f(n)\).
Compare with \(\frac{n(n-1)}{2}\).
\(f(n)-\frac{n(n-1)}{2}\) is additive and equals \(1\) at \(n=1\). Answer: \(f(n)=\frac{n(n+1)}{2}\).
Mock olympiad problem. Tags: functional-equation.