If I was a full-time student from August 22,2016-Dec 2016, does that count as 4 or 5 months for the retirement contribution credit?

[dmertz]

That's 5 months because you were a full-time student at least part of each of 5 calendar months.  You are ineligible for the Retirement Savings Contributions Credit.

From IRS Pub 590-A:

Full-time student. You are a full-time student if, during some part of each of 5 calendar months (not necessarily consecutive) during the calendar year, you are either:

• A full-time student at a school that has a regular teaching staff, course of study, and regularly enrolled body of students in attendance, or
• A student taking a full-time, on-farm training course given by either a school that has a regular teaching staff, course of study, and regularly enrolled body of students in attendance, or a state, county, or local government.

You are a full-time student if you are enrolled for the number of hours or courses the school considers to be full time.