\[a = 2k;\ \ b = 2d;\ \ где\ \ k,d \in Z\]
\[a^{2} + b^{2} = (2k)^{2} + (2d)^{2} =\]
\[= 4k^{2} + 4d^{2} = 2\left( 2k^{2} + 2d^{2} \right)\]
\(\Longrightarrow четное\ число.\)