MathDB

In a town every two residents who are not friends have a friend in common, and no one is a friend of everyone else. Let us number the residents from

1

n

and let

a_i

be the number of friends of the

i^{\text{th}}

resident. Suppose that

\sum_{i=1}^{n}a_i^2=n^2-n

Let

k

be the smallest number of residents (at least three) who can be seated at a round table in such a way that any two neighbors are friends. Determine all possible values of

k.

Problem Statement