Use predicates, quantifiers, logical connectives, and mathematical operators to express the statement that “Every positive integer is the sum of the squares of four integers.

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Let $x$ is a number.

“Every positive integer is the sum of the squares of four integers" is

$\forall x\in N \exist a\in Z \exist b\in Z \exist c\in Z \exist d\in Z\,x=a^2+b^2+c^2+d^2$