MathDB

Let

(x_1, y_1)

(x_2, y_2)

(x_3, y_3)

(x_4, y_4)

, and

(x_5, y_5)

be the vertices of a regular pentagon centered at

(0, 0)

. Compute the product of all positive integers k such that the equality

x_1^k+x_2^k+x_3^k+x_4^k+x_5^k=y_1^k+y_2^k+y_3^k+y_4^k+y_5^k

must hold for all possible choices of the pentagon.

Problem Statement