4

Part of 2010 Albania Team Selection Test

Problems(1)

Albanian IMO TST 2010 Question 4

Source:

\sigma (n)

we denote the sum of natural divisors of the natural number

n

. Prove that, if

n

is the product of different prime numbers of the form

2^k-1

k \in \mathbb{N}

Mersenne's

prime numbers) , than

\sigma (n)=2^m

m \in \mathbb{N}

. Is the inverse statement true?

algebrapolynomialfunctioninequalitiesnumber theoryprime numbersnumber theory unsolved