[2.4] Exercise 8
For a given set \(N\), there can be at most one set \(M\) such that \(N,M\) is an Euler pair. Why? Think backward: "If there were two different such sets, \(M\) and \(M'\), then there would have to be some smallest integer.
Example 1
$$
\begin{align}
6 &= 1 + 1 + 1 + 1 + 1 + 1 \\
6 &= 2 + 2 + 1 + 1 \\
6 &= 2 + 1 + 1 + 1 + 1 \\
6 &= 4 + 1 + 1 \\
6 &= 4 + 2 \\
6 &= 3 + 1 + 1 + 1 \\
6 &= 3 + 2 + 1 \\
6 &= 3 + 3 \\
6 &= 2 + 2 + 2 \\
6 &= 5 + 1 \\
6 &= 6
\end{align}
$$