Answer to Question #251383 in Discrete Mathematics for Faiz

Question

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.

Answer 1

Let $x$ is a number.

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

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