Question 92
Observe that
$$\begin{gathered}1^2+2^2+(1\times2)^2=3^2\\2^2+3^2+(2\times3)^2=7^2\\3^2+4^2+(3\times4)^2=13^2.\end{gathered}$$
Prove that if $a,b$ are consecutive integers, then $a^2+b^2+(ab)^2$ is a perfect square.
$$\begin{gathered}1^2+2^2+(1\times2)^2=3^2\\2^2+3^2+(2\times3)^2=7^2\\3^2+4^2+(3\times4)^2=13^2.\end{gathered}$$
Prove that if $a,b$ are consecutive integers, then $a^2+b^2+(ab)^2$ is a perfect square.