Polynomial factor-Nightmare

Algebra Level 5

If \({ x }^{ 2 }-x-1\) is a factor of \({ zx }^{ 20 }+{ yx }^{ 19 }+1,\) then what is the value of \(\lvert z\rvert?\)

Note: \(x\) is a variable, while \(y\) and \(z\) are constants.

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