Which of the following statements about Java's equals() and hashCode() methods is correct?

A) The hashCode() method must always return the same integer for the same object during a single execution of a Java application, regardless of whether the object is modified.
B) If two objects are equal according to the equals() method, they must return the same hash code value as defined by the hashCode() method.
C) It is permissible for two objects to have the same hash code value but not be equal according to the equals() method.
D) Both equals() and hashCode() methods must be overridden together for all classes in Java.