MathDB

VMO 2016 Problem 7

Source: VMO 2016

January 7, 2016

number theoryperfect number

Problem Statement

a) Prove that if

n

is an odd perfect number then

n

has the following form

n=p^sm^2

where

p

is prime has form

4k+1

,

s

is positive integers has form

4h+1

, and

m\in\mathbb{Z}^+

,

\frac{n(n+1)}{2}

is not divisible by

p

. b) Find all

n\in\mathbb{Z}^+

,

n>1

such that

n-1

and

\frac{n(n+1)}{2}

is perfect number

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