G2.4 Let $d$ be an odd prime number. If $89-(d+3)^{2}$ is the square of an integer, find the value of $d$.
$\because d$ is odd, $d+3$ must be even, $89-(d+3)^{2}$ must be odd.
$$
89=(d+3)^{2}+m^{2}
$$

By trial and error, $m=5,89=8^{2}+5^{2}$
$$
\begin{array}{l}
\Rightarrow d+3=8 \\
\Rightarrow d=5
\end{array}
$$