MathDB

On a circle with radius

1

the points

A_1, A_2,..., A_n

lie such that every arc

A_iA_{i+i}

has length

\frac{2\pi}{n}= a

. Given that there exists a set

V

consisting of

k

of these points (

k < n

), which has the property that each of the arc lengths

a

2a

,...

(n- 1)a

can be obtained in exactly one way be taken as the length of an arc traversed in a positive sense, beginning and ending in a point of

V

. Express

n

in terms of

k

and give the set

V

for the case

n = 7

Problem Statement