MathDB

Let

n

and

a \leq n

be two positive integers. There's

2n

people sitting around a circle reqularly. Two people are friend iff one of their distance in the circle is

a

(that is ,

a-1

people are between them). Find all integers

a

in terms of

n

st we can choose

n

of these people , no two of them positioned in front of each other(means they're not antipodes of each other in the circle) and the total friendship between them is an odd number.

Problem Statement