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#### jakncoke

##### Active member

- Jan 11, 2013

- 68

Let v be a fixed vector $\in \mathbb{F}_p^{n}$, Let M be a nxn matrix with entries from $\mathbb{F}_p$. Define G:$\mathbb{F}_p^{n} \to \mathbb{F}_p^{n}$ by

G(x) = v + Mx. Define the k-fold composition of G by itself by $G^{1}(x) = G(x)$

and $G^{k+1} = G (G^{k}(x))$ Determine all pairs p,n for which there exists a vector v and a matrix M such that the $p^n$ vectors of $G^{k}(0), k=1,...,p^{n}$ are distinct.