You can have the program installed and activated on up to two computers at a time.
True, Adobe allows you to have the same purchased activated serial number on no more than 2 of your computers. According to the License Agreement, the two are not to be used at the same time.
But, the important question is what is the operating system of computer 1. Are you using installation files from a purchased download or installation discs from purchase of boxed packaging of the product? Installation files from download will be specific to computer operating system to which the installation files are downloaded; whereas, boxed packaging gives you installation disc for Windows and Mac.