Let n≥2 be an integer and let a1,a2,⋯an be fixed positive integers (not necessarily all distinct) in such a way that gcd(a1,a2⋯an)=1. In a board the numbers a1,a2⋯an are all written along with a positive integer x. A move consists of choosing two numbers a>b from the n+1 numbers in the board and replace them with a−b,2b. Find all possible values of x, with respect of the values of a1,a2⋯an, for which it is possible to achieve a finite sequence of moves (possibly none) such that eventually all numbers written in the board are equal. combinatoricsnumber theory