French language Q&A Forum

Or there must be a preposition in between noun and 'penser', which means only either 'penser à + noun' or 'penser de + noun' ?

If 'penser+noun' exist, how to differentiate 'penser+noun' and 'penser à + noun'? 

Let's say I have a Mathematic problem and I am thinking/reflecting on it, hoping to come out with a solution. It should be 'penser' the mathematic problem or 'penser à' the mathematic problem?

If I finally think of the solution, is it correct to use 'penser à' the solution?

Thank you

Just to be clear, in expressions like : 'Je vais au cinéma pour voir un film' ... presumably this implies that it is wrong to just say 'Je vais au cinéma voir un film'