Answer
$\forall x ((x>0) \rightarrow x=a^{2}+b^{2}+c^{2}+d^{2})$
Work Step by Step
Let the domain be all integers.
An integer is positive, if the integer is larger than 0.
We can rewrite the given sentence as: “For all integers x, if x is positive, then there exists four integers a, b, c and d such that x is the sum of the squares of the four integers.“
$\forall x ((x>0) \rightarrow x=a^{2}+b^{2}+c^{2}+d^{2})$
