How to write Fermat's Last Theorem using quantifiers?

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How do I write Fermat's Last Theorem using only universal and existential quantifiers.

I only want to quantify it over the natural numbers (excluding zero)- for which I use $ℤ+$ to represent this set. My attempt at it, which I don't think is right, is this:

$∀(x∈ℤ+) ∀(y∈ℤ+) ∀(z∈ℤ+) ∃(n∈ℤ+) (x^n+y^n=z^n → n<3)$