Write the following statements in predicate form, using logical operators $\land, \lor$, (NOT - negation but don't know where the symbol is :/) ($\color{blue}{\text{edit: it is }\neg}$ \neg), and quantifiers $\forall,\exists $. Below $\Bbb Z^+$ denotes all positive integers $\{1,2,3,\ldots\}$.
I need help with this first statement: For any $(x, y) \in {\Bbb Z^+}^2$ the equation $x^2 + y^2 - z = 0$ has a solution $z \in\Bbb Z^+ $
$$ (\forall x,y\in\mathbb{Z^+})(\exists z\in\mathbb{Z^+})(x^2+y^2-z=0) $$