SIMON-MARAIS 2024 B2

Determine all continuous functions $f : \mathbb{R} \setminus \{1\} \rightarrow \mathbb{R}$ that satisfy

$f(x) = (x + 1)f(x^2),$

for all $x \in \mathbb{R} \setminus \{-1, 1\}$ .

A model read this text from the scan of the paper by OCR, with vision/local (GLM-OCR-8bit). No person has checked it against the paper yet.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.