2018/01/18 by Aldi Nestor de Souza, de Souza, Aldi Nestor
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1801.06182
openalex publication_date 2018/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The existence of a perfect odd number is an old open problem of number theory. An Euler's theorem states that if an odd integer n is perfect, then n is written as n = p ^ rm ^ 2 , where r, m are odd numbers, p is a prime number of the form 4 k + 1 and (p, m) = 1 , where (x, y) denotes the greatest common divisor of x and y . In this article we show that the exponent r , of p , in this equation, is necessarily equal to 1. That is, if n is an odd perfect number, then n is written as n = pm ^ 2.