It works for you because your code does not use any functionality (HashMap, HashTable) which needs the hashCode() API.
However, you don’t know whether your class (presumably not written as a one-off) will be later called in a code that does indeed use its objects as hash key, in which case things will be affected.
As per the documentation for Object class:
The general contract of hashCode is:
Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
If two objects are equal according to the equals(Object) method, then calling the hashCode method on each of the two objects must produce the same integer result.