MathDB
Relations involving the sum of divisors

Source: Romania TST 3 2010, Problem 3

August 25, 2012
modular arithmeticarithmetic sequencenumber theory proposednumber theory

Problem Statement

Given a positive integer aa, prove that σ(am)<σ(am+1)\sigma(am) < \sigma(am + 1) for infinitely many positive integers mm. (Here σ(n)\sigma(n) is the sum of all positive divisors of the positive integer number nn.)
Vlad Matei