# Solution:2010-19 Fixed Points

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 $A^k u = u.$

The best solution was submitted by Chiheon Kim (김치헌), 수리과학과 2006학번. Congratulations!

Here is his Solution of Problem 2010-19.

An alternative solution was submitted by 박민재 (KSA-한국과학영재학교, +3).

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