1

Part of 1990 Polish MO Finals

Problems(2)

functional equation in R

Source: Problem 1, Polish NO 1990

Find all functions

f : \mathbb{R} \longrightarrow \mathbb{R}

(x - y)f(x + y) - (x + y)f(x - y) = 4xy(x^2 - y^2)

functionalgebrafunctional equationalgebra unsolved

Triangle inscribed in a square

Source: Problem 4, Polish NO 1990

A triangle whose all sides have length not smaller than

1

is inscribed in a square of side length

1

. Prove that the center of the square lies inside the triangle or on its boundary.

geometry unsolvedgeometry