We present three new methods that investigate the equalities implied by a system of linear arithmetic constraints. Implied equalities can be used to simplify linear arithmetic constraints and are valuable in the context of Nelson-Oppen style combinations of theories. The first method efficiently checks whether a system of linear arithmetic constraints implies an equality at all. In case the system does, the method also returns a valid equality as an explanation. The second method uses the first method to compute a basis for all implied equalities, i.e., a finite representation of all equalities implied by the linear arithmetic constraints. The third method uses the second method to check efficiently whether a system of linear arithmetic constraints implies a given equality.