# RMO Practice Problems - Number Theory #4

**Number Theory**Level 5

Find the sum of all positive integers \(x, y ,z\) such that \(x \leq y \leq z\) and \[x^{y} + y^{z} = z^{x}\]

**Details and Assumptions:**

- If you get the solutions as (\(1,3,10\)) and (\(2,3,16\)). Then give your answer as the sum of all \(x,y,z\) i.e. \(1+3+10+2+3+16=35\).