Potencias de números enteros como suma de impares consecutivos

Abstract

In this paper it is demonstrated that the power (p + q) of a natural number (n), can be derived as the sum of a series of consecutive odd numbers. The series of the summation is conditioned by a lower and upper boundary, being equal to half the difference plus 1, and respectively half the sum of the powers p and q of the natural number. The algorithm, notwithstanding its simplicity, offers some interesting opportunities in the applications of number theory to numerical analysis.