# Solution: 2008-12 Finding eigenvalues and eigenvectors

Find all real numbers $$\lambda$$ and the corresponding functions $$f$$ such that the equation
$$\displaystyle \int_0^1 \min(x,y) f(y) \,dy=\lambda f(x)$$
has a non-zero solution $$f$$ that is continuous on the interval [0,1].

The best solution was submitted by Haewon Yoon (윤혜원), 수리과학과 2004학번. Congratulations!

Here is his Solution of Problem 2008-12.

GD Star Rating

# Solution: 2008-7 Find all real solutions

Find all real solutions of $$3^x + 5^{x^2} = 4^x + 4^{x^2}$$.

The best solution was submitted by Haewon Yoon (윤혜원), 수리과학과 2004학번. Congratulations!

Here is his Solution of 2008-7.

GD Star Rating

# Solution: 2008-5 Monochromatic lines

Suppose that P is a finite set of points in the plane colored by red or blue. Show that if no straight line contains all points of P, then there exists a straight line L with at least two points of P on L such that all points on $$P\cap L$$ have the same color.

The best solution was submitted by Haewon Yoon (윤혜원), 수리과학과 2004학번. Congratulations!

GD Star Rating
Let A, B be $$3\times 3$$ integer matrices such that A, A+B, A+2B, A+3B, A-B, A-2B, A-3B are invertible and their inverse matrices are all integer matrices.