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v2 of sum of divisors

Source: Romania 2018 TST Problem 4 Day 3

May 25, 2020

number theorysum of divisors

Problem Statement

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

\frac {2^k{\sigma({s})}} {s}

are odd for every

s \in S

.

\sigma({s})

is the sum of all positive integers of

s

(1 and

s

included).

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