2015 UMO Problems/Problem 1


Three trolls have divided $n$ pancakes among themselves such that:

• Each troll has a positive integer number of pancakes.

• The greatest common divisor of the number of pancakes held by any two trolls is bigger than $1$.

• The three greatest common divisors obtained in this way are all distinct.

What is the smallest possible value of $n$?


See Also

2015 UMO (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6
All UMO Problems and Solutions