Is this the correct logical notation for this English statement?

Question

Is this the correct logical notation for this English statement?

Statement in english: "there are no integers x and y such that x^2=4y+2"

Logical equivalent? (where Z represents integers and P(x,y) is x^2=4y+2 ): ∀x∀y ∈ Ζ, ¬P(x,y)

Answer 1

Some other ways that you could write that statement are:

∀x, y ∈ Z, x² ≠ 4y+2

∄x, y ∈ Z: x² = 4y+2

I think the first version is more common than the second.