MathDB

4b

Part of 2011 Abels Math Contest (Norwegian MO)

Problems(1)

in 199 persons, each person is a friend of exactly 100 others

Source: Norwegian Mathematical Olympiad 2011 - Abel Competition p4b

9/4/2019
In a group of 199199 persons, each person is a friend of exactly 100100 other persons in the group. All friendships are mutual, and we do not count a person as a friend of himself/herself. For which integers k>1k > 1 is the existence of kk persons, all being friends of each other, guaranteed?
combinatorics