## Problem of the week

### 2022-16 Identity for continuous functions

For a positive integer $$n$$, find all continuous functions $$f: \mathbb{R} \to \mathbb{R}$$ such that
$\sum_{k=0}^n \binom{n}{k} f(x^{2^k}) = 0$
for all $$x \in \mathbb{R}$$.