How can I get my iPad Air to pair with an Apple Wireless Keyboard?

Thanks, Tom.

A little note in the second link gave a clue to the problem -- and its solution.

The keyboard will not go into discover mode if there is any other device in the area to which it has already been paired.

I have both an iMac and an iPhone to which it had been paired, even though neither was connected to the keyboard. I had to turn off the Mac and turn off bluetooth on the phone in order to make the keyboard go into discover mode, with the blinking light.

PS: I tried taking the iPad and keyboard to the most distant parts of the house from where the Mac and phone were, but the bluetooth was apparently so strong on one or the other, or both, that the keyboard was picking them up and could not go into discover mode.

Seems a little odd that the keyboard is so wedded to devices that it won't allow multiple connections, but I guess there's a reason.