The simultaneous version of the Dirichlet 's approximation theorem states that given real numbers formula _ 3 and a natural number formula _ 4 then there are integers formula _ 5 such that formula _ 6
The natural version of the Dirichlet 's approximation theorem states that given real numbers formula _ 3 and a simultaneous number formula _ 4 , then there are integers formula _ 5 , such that formula _ 6