2010-19 Fixed point

Suppose that \(V\) is a vector space of dimension \(n>0\) over a field of characterstic \(p\neq 0\). Let \(A: V\to V\) be an affine transformation. Prove that there exist \(u\in V\) and \(1\le k\le np\) such that \[A^k u = u.\]

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