Problem

Source: XIII International Festival of Young Mathematicians Sozopol 2024, Theme for 10-12 grade

Tags: functional equation, algebra



Find all functions \(f:\mathbb{R}^{+} \to \mathbb{R}^{+}\) such that \[ f(x) > x \ \ \text{and} \ \ f(x-y+xy+f(y)) = f(x+y) + xf(y) \]for arbitrary positive real numbers \(x\) and \(y\).