# 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).

GD Star Rating
loading...

# 2010-20 Monochromatic line

Let X be a finite set of points on the plane such that each point in X is colored with red or blue and there is no line having all points in X. Prove that there is a line L having at least two points of X such that all points in L∩X have the same color.

GD Star Rating
loading...