# warning messages – Using the solve function to extract solutions to an equation in natural numbers

I have the following code:

``````n /. Solve({c == 1/2 (-2 + 3 n^2) (-1 + 3 n^2) (1 - 3 n + 3 n^3),
n (Element) PositiveIntegers}, n)((1))
``````

This procudes the number $$n$$ such that the equation is solved in the natural numbers because $$cinmathbb{N}$$. However when there is no solution found the code gives an error message:

``````Part::partw: Part 1 of {} does not exist.
ReplaceAll::reps: {{}((1))} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
``````

How can I write code that gives $$n$$ when it exists and it gives $$0$$ if no solution exists? So for example when $$c=1045$$ we see that $$n=2inmathbb{N}$$ so the code must give `2` as the output but when $$c=1046$$ there is no $$ninmathbb{N}$$ that solves the equation so the code must give `0`.