I have these kinds of expressions:
Correct expressions (true and valid) $$\begin{align} 3 &= 3\hbox{ (it's obvious, isn't it?)}\\ 4 &= 1 + 3\\ 8 &= 5\\ 9 &= 1 + 5\\ 12 &= 1 + 3 + 5\\ 18 &= 4 + 6 \end{align}$$
True but not valid expressions $$\begin{align} 3 &= 1 + 2\\ 10 &= 4 + 4\\ 12 &= 5 + 3 + 1\\ 14 &= 1 + 4 + 5 \end{align}$$
Incorrect expressions (false and invalid) $$\begin{align} 10 &= 4 + 6\\ 11 &= 5 + 6 \end{align}$$
For each non-negative integer in the left side, there is a unique expression on the right side.
Can you tell what is the general rule? I think it is an easy one for you, guys, but feel free to ask for specific values if you need them.