186. Exact Squares. Find four numbers, the sum of each pair of which, as well as their total sum, are exact squares.
186. Of course, several solutions to this problem can be found, but apparently the smallest numbers will be:

\[
\begin{aligned}
a & =10430, \quad b=3970, \quad c=2114, \quad d=386 \\
a+b & =10430+3970=14400=120^{2} \\
a+c & =10430+2114=12544=112^{2} \\
a+d & =10430+386=10816=104^{2} \\
b+c & =3970+2114=6084=78^{2} \\
b+d & =3970+386=4356=66^{2} \\
c+d & =2114+386=2500=50^{2} \\
a+b+c+d & =10430+3970+2114+386=16900=130^{2}
\end{aligned}
\]

In finding the general solution, the fact is used that any prime number of the form \(4 m+1\) is a sum of squares. Perhaps the reader will want to find this solution.