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sum of positive divisors coprime with the number

Source: Tuymaada 2017 Seniors Q6 (day 2 P2)

September 26, 2017

number theorysum of divisorscoprime

Problem Statement

Let

\sigma(n)

denote the sum of positive divisors of a number

n

. A positive integer

N=2^r b

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.
(J. Antalan, J. Dris)

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