MathDB

6

Part of 2017 Tuymaada Olympiad

Problems(2)

Sum of divisors

Source: Tuymaada 2017 Junior Level

7/18/2017
Let σ(n)\sigma(n) denote the sum of positive divisors of a number nn . A positive integer N=2rbN=2^rb is given,where rr and bb are positive integers and bb is odd. It is known that σ(N)=2N−1\sigma(N)=2N-1. Prove that bb and σ(b)\sigma (b) are coprime.
Tuymaada Q6 Juniors
number theory
sum of positive divisors coprime with the number

Source: Tuymaada 2017 Seniors Q6 (day 2 P2)

9/26/2017
Let σ(n)\sigma(n) denote the sum of positive divisors of a number nn. A positive integer N=2rbN=2^r b is given, where rr and bb are positive integers and bb is odd. It is known that σ(N)=2N−1\sigma(N)=2N-1. Prove that bb and σ(b)\sigma(b) are coprime.
(J. Antalan, J. Dris)
number theorysum of divisorscoprime