Problem

Source: Indonesian TST for IMO 2023 Stage 1: Test 3 - Algebra

Tags: function, functional equation, algebra



Find all function $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfied \[f(x+y) + f(x)f(y) = f(xy) + 1 \]$\forall x, y \in \mathbb{R}$