This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
In strict sense, technically its not mandatory. Neither overriding Hashcode when equals is overriden or vice versa.
But, on design level, there is a contract between equals and hashcode. Whenever equals method confirms two objects as same, they should return the same hashcode too. But its not the other way around.
Therefore its a good programming practice to override hashcode as well if you decide to override equals method.
In case you are overriding hashcode only, its your choice to override equal or not for your own sake.
Just FYI : Hashcode helps in efficient hashing for Hashmap and other such collections, while equals confirm the equalness of two objects actual value per se.