Isn't the left side bigger?

Number Theory Level 4

\[ \large { 4 }^{ x }+{ 5 }^{ y }={ 3 }^{ z } \]

For non-negative integers \(x,y,z\), let triplets \(\left\{ { x }_{ 1 },{ y }_{ 1 },{ z }_{ 1 } \right\} ,\left\{ { x }_{ 2 },{ y }_{ 2 },{ z }_{ 2 } \right\} \ldots \left\{ { x }_{ n },{ y }_{ n },{ z }_{ n } \right\} \) be the solutions to the equation above,

Submit your answer as \(\displaystyle \sum _{ i=1 }^{ n }( { { x }_{ i }+{ y }_{ i }+{ z }_{ i } } )\).

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