MathDB

The following problem is open in the sense that no solution is currently known to part (b).
Let

n\geq 2

be an integer, and

P_n

be a regular polygon with

n^2-n+1

vertices. We say that

n

is \emph{taut} if it is possible to choose

n

of the vertices of

P_n

such that the pairwise distances between the chosen vertices are all distinct.
(a) show that if

n-1

is prime then

n

is taut. (b) Which integers

n\geq 2

are taut?

Problem Statement