When you are covered by any part of Medicare, you become ineligible to contribute to an HSA. It does not matter which Part.
Note that this is also true if, when you sign up, the Social Security Administration backdates your application by 6 months, as they do for some retirees.
In this case, the ineligibility begins with the first month of Medicare coverage, not when you signed up.
Note that it is the coverage on the first day of the month that determines the coverage for the month.
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