In addition to these "elements of proof," adultery is one of the hardest offenses to prove. The prosecution must prove sexual intercourse, which usually means they must have a confession or photos. The mere fact that two people are living together is not sufficient to prove sexual intercourse.
Interestingly, in the military, a single person can be charged with this offense. If a single person has an affair with a married person, under circumstances which are determined to be prejudicial to good order and discipline, or of a nature to bring discredit upon the armed forces, they can be charged with adultery.
For complete details, see our article about Adultery in the Military.