Suppose that \(x,y,z\) are positive integers satisfying \(x \le y \le z\), and such that the product of all three numbers is twice their sum. What is the sum of all possible values of \(z\)?

abcdefghijklmnopqrst Nov 25, 2021

#1**0 **

The only triple that works is (x,y,z) = (2,2,4), so the sum of all possibe values of z is 4.

Guest Nov 25, 2021