Are there enough Wild Artifacts in the game?

I wonder if there are enough Wild Artifacts to find in the game or do I have to buy more than one from Serendipity. 75K gil, if you're not kissed by lady luck, is quite expensive. I think I have found all of them (not bought one yet) but I still have a bunch of portals to open (around 5 locations more to discover).

Does a player who wants to explore all the Historia Crux have to buy more than 1 artifact in order to complete the game?

There are exactly enough wild artefacts including the ones you can buy from Serendipity to open all the gates. So you will have to spend 75k gil on a artefact.