That's a good question. You would get the extra lan for +2 int. I see a few ways to handle Linguistic's "Learn a Language: Whenever you put a rank into this skill, you learn to speak and read a new language."
1- You list 20 languages in order and they get 1 for every level they have.
2- You throw a book at the player for even suggesting such a combo :)
3- You disallow the linguistics skill in headbands as being "not worth the headache"
4- Allow the linguistics skill, but not the "Learn a Language" part.
5- like 1 but let them choose from the list of 20 languages.
I agree with Mosaic and suspect RAW would be 1, but I doubt you will find an answer to this question.
Side question; has anyone seen a headband with the linguistics skill in any published pathfinder product?
I was hoping for the old 3.5 interpretation, but the errata make it pretty clear:
FAQ/Errata
If I wear a headband of vast intelligence, do I get retroactive skill ranks for my Int increase in addition to the skill ranks associated with the item?
No. The skill associated with the magic item represents the “retroactive” skill ranks you’d get from the item increasing your Intelligence. You don’t get the item’s built-in skill ranks and another set to assign however you want.
[ Source]
https://www.d20pfsrd.com/magic-items/wondrous-items/h-l/headband-of-vast-in telligence
