Atresvido numbers
Source: 22nd Iberoamerican Olympiad 2007, problem 5
September 13, 2007
group theoryabstract algebrainequalitiesgeometrygeometric transformationnumber theory proposednumber theory
Problem Statement
Let's say a positive integer is atresvido if the set of its divisors (including 1 and ) can be split in in 3 subsets such that the sum of the elements of each is the same. Determine the least number of divisors an atresvido number can have.