Mac App Store says I need an update even though it's already installed
I have a red badge with the number 1 on the App Store icon on my dock (MacBook Pro, Mountain Lion). When I click on it, it searches and shows me a single application, but also tells me (correctly, too) that the application is installed. How do I get rid of the badge and convince App Store that I need no updates? I have quit everything and rebooted and it still shows up that way.
MacBook Pro, OS X Mountain Lion