A.B.C. Algebra

The expression is equivalent to saying:

$a^2 + b^2 = c^2$

The smallest Pythagorean triple with all integers is $(3, 4, 5)$

$(3)^2 + (4)^2 = (5)^2$

After comparison of the equations, this implies the result:

$\boxed{c = 5}$

If $a^{2}+b^{2}=c^{2}$ and $a$ , $b$ , $c>0$ , then $a$ , $b$ , and $c$ is a Pythagorean triple. The Pythagorean triple with the smallest $c$ value is $3$ , $4$ , and $5$ . Thus, $\boxed{c=5}$ .