Are two Java objects with same hashcodes not necessarily equal?

According to the Javadoc in: http://download.oracle.com/javase/6/docs/api/java/lang/Object.html#hashCode%28%29

It is not required that if two objects are unequal according to the equals(java.lang.Object) method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hashtables.

Edit: In the real world two Strings may have the same hash code. For instance, if you want to store all string combinations that contain lowercase English letters (like "aaaaaaaaaa","aaaaaaaaab" and so on) of length 10, you can't assign a unique hash code to each of the 141.167.095.653.376 combinations, since int in Java is 32-bit and, therefore, can have up to 4.294.967.296 distinct values.

The purpose of the hashCode function is allow objects to be quickly partitioned into sets of things that are known to unequal to all items outside their own set. Suppose one has 1,000 items and one divides them into ten roughly-equal-sized sets. One call to hashCode could quickly identify the item as being not equal to 900 of the items, without having to use equals on any of those items. Even if one had to use equals to compare the item to 100 other items, that would still be only 1/10 the cost of comparing it to all 1000 items. In practice, even in a large collection, hashCode will often eliminate 99.9% or more of the unequal items, leaving at most a handful to be examined.

If two objects have the same hashcode then they are NOT necessarily equal. Otherwise you will have discovered the perfect hash function.

But the opposite is true: if the objects are equal, then they must have the same hashcode.