RMO Practice Problems - Number Theory #4

Find the sum of all positive integers x,y,zx, y ,z such that xyzx \leq y \leq z and xy+yz=zxx^{y} + y^{z} = z^{x}

Details and Assumptions:

  • If you get the solutions as (1,3,101,3,10) and (2,3,162,3,16). Then give your answer as the sum of all x,y,zx,y,z i.e. 1+3+10+2+3+16=351+3+10+2+3+16=35.

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