# 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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