# RMO Practice Problems - Number Theory #4

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. $$1+3+10+2+3+16=35$$.

×