Given two positives integers m and n, prove that there exists a positive integer k and a set S of at least m multiples of n such that the numbers 2kσ(s)s are odd for every s∈S. σ(s) is the sum of all positive integers of s (1 and s included).
Source: Romania 2018 TST Problem 4 Day 3
Tags: number theory, sum of divisors
Given two positives integers m and n, prove that there exists a positive integer k and a set S of at least m multiples of n such that the numbers 2kσ(s)s are odd for every s∈S. σ(s) is the sum of all positive integers of s (1 and s included).