On the cubic nature of the number 1-p

Abstract

This article gives a purely arithmetic method for obtaining the cubic character of the number 1—ᵽ. The method is based on the well-known Gauss lemma. For clarity, the author presents the numbers ɑ+βp, where ɑ and β are real as points of the plane. Thus, the problem comes down to finding the number of lattice points in a certain area. The result is achieved through a specific choice of fundamental area and appropriate division into parts.