MathDB

6

Part of 2009 Saint Petersburg Mathematical Olympiad

Problems(2)

Color graph

Source: St Petersburg Olympiad 2009, Grade 11, P6

8/30/2017
Some cities in country are connected by road, and from every city goes ≥2008\geq 2008 roads. Every road is colored in one of two colors. Prove, that exists cycle without self-intersections ,where ≥504\geq 504 roads and all roads are same color.
combinatoricsgraph theory
Periodic sequence

Source: St Petersburg Olympiad 2009, Grade 10, P6

8/30/2017
(xn)(x_n) is sequence, such that xn+2=∣xn+1∣−xnx_{n+2}=|x_{n+1}|-x_n. Prove, that it is periodic.
algebra