MathDB

2

Part of 2009 China National Olympiad

Problems(2)

Prime number

Source: Chinese National Olympiad 2009 P2

1/10/2009
Find all the pairs of prime numbers (p,q) (p,q) such that pq|5^p\plus{}5^q.
number theoryrelatively primenumber theory proposed
Coloring

Source: Chinese National Olympiad 2009 P5

1/10/2009
Let P P be a convex n n polygon each of which sides and diagnoals is colored with one of n n distinct colors. For which n n does: there exists a coloring method such that for any three of n n colors, we can always find one triangle whose vertices is of P P' and whose sides is colored by the three colors respectively.
combinatorics proposedcombinatorics