Transforming predicate form to quantifiers

[MarcL]

Homework Statement

Write the following statements in predicate form, using logical operators ^,∨, (NOT - negation but don't know where the symbol is :/) , and quantifiers ∀,∃. Below ℤ⁺ denotes all positive integers {1,2,3,...}.

I need help with this first statement:
For any x, y ∈ ℤ⁺ the equation x² + y² - z = 0 has a solution z
∈ ℤ⁺

Homework Equations

The fact that ∀ is universal and ∃ is existential.

The Attempt at a Solution

I can't seem to figure out where to start... I just got ∀x∀y ( x² + y² = z) which seems wrong to me. any help?

 

[Stephen Tashi]

"Has a solution" means "there exists a solution".