Perfect Numbers
Source: Saudi Arabia IMO TST Day III Problem 1
July 22, 2014
number theory unsolvednumber theory
Problem Statement
A perfect number is an integer that equals half the sum of its positive divisors. For example, because , is a perfect number.[*] (a) A square-free integer is an integer not divisible by a square of any prime number. Find all square-free integers that are perfect numbers.[*] (b) Prove that no perfect square is a perfect number.