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. \(1+3+10+2+3+16=35\).

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