Show that ∃n∃m (n² + m² = 6) is False

Section 1.4
27f. Prove that ∃n∃m (n² + m² = 6) is False.

The only possible pairs of integers whose sum is 6 are 1+5, 2+4, and 3+3. Since none of 2, 3, or 5 are squares of integers, then clearly the pairs of integers whose sum is 6 are not solutions that satisfy ∃n∃m (n² + m² = 6).