in 199 persons, each person is a friend of exactly 100 others
Source: Norwegian Mathematical Olympiad 2011 - Abel Competition p4b
September 4, 2019
combinatorics
Problem Statement
In a group of persons, each person is a friend of exactly 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 is the existence of persons, all being friends of each other, guaranteed?