Suppose (for this question only) that $h$ is the function $x \mapsto x$. Determine a solution of $(E_{h})$: $$\forall x \in \mathbb{K},\, f(x+1) - f(x) = x$$ in $\mathbb{K}_{2}[X]$, then all polynomial solutions of the equation $(E_{h})$.
Suppose (for this question only) that $h$ is the function $x \mapsto x$. Determine a solution of $(E_{h})$:
$$\forall x \in \mathbb{K},\, f(x+1) - f(x) = x$$
in $\mathbb{K}_{2}[X]$, then all polynomial solutions of the equation $(E_{h})$.