MathDB

Let

n \ge 4

be a natural number. Let A_1A_2 \cdots A_n be a regular polygon and

X = \{ 1,2,3....,n \}

. A subset

\{ i_1, i_2,\cdots, i_k \}

X

, with k \ge 3 and i_1 < i_2 < \cdots < i_k, is called a good subset if the angles of the polygon A_{i_1}A_{i_2}\cdots A_{i_k} , when arranged in the increasing order, are in an arithmetic progression. If

n

is a prime, show that a proper good subset of

X

contains exactly four elements.

Problem Statement