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Sum of divisors

Source: Tuymaada 2017 Junior Level

July 18, 2017

number theory

Problem Statement

Let

\sigma(n)

denote the sum of positive divisors of a number

n

. A positive integer

N=2^rb

is given,where

r

and

b

are positive integers and

b

is odd. It is known that

\sigma(N)=2N-1

. Prove that

b

and

\sigma (b)

are coprime.
Tuymaada Q6 Juniors

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