Downloading Flashplayer - how can it be this hard???

I have an Apple ID and password.

I have an Adobe ID and password. 

Both work when I sign on to those websites.

In an attempt to download flash player onto my MacBook Air, it will not accept my adobe password.  When I attempt to change it, it asks for my Apple ID and password.  When I type it in, it still won't let me change it.

What am I doing wrong????

Thanks.