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When you override equals() you should also override hashCode(). The reason will be shortly clear.

The following rule must be always true:

When a.equals(b) then a.hashCode() = b.hashCode()

Most collections use equals() to find or remove elements.

The hashCode() is used to insert values into a HashTable, HashMap or HashSet. An hash table uses an hash key to store values internally into a bucket. Each bucket contain might contains a group of values, so at this point equals() is used to find the exact match. This is the reason the two calls work togheter.

Consider that == is different than equals(), because the first compare the references, not their content. However, the default implementation of equals() in the class Object, use the == operator.

It is not true that hashCode provides a unique identifier for an object, but equal objects must have same hash code.

This is an example of a class that overrides the two methods:

public class Person {

	private int id;
	private String name;

	public boolean equals(Object o){

		if (o == this) return true;

		if(!(o instanceof Person)) return false;

		Person other = (Person) o;

               if (this.id != other.id) {
                  return false;
               }
     
               if ((this.name == null) ? (other.name != null) : !this.name.equals(other.name)) {
                  return false;
               }

		return true;
	}

	public int hashCode(){
		int result = 17;
     
		result = 31 * result + this.id;
                hash = 31 * hash + (this.name != null ? this.name.hashCode() : 0);

		return result;
	}

	public String getName() {
		return name;
	}

	public void setName(String name) {
		this.name = name;
	}

	public int getId() {
		return id;
	}

	public void setId(int id) {
		this.id = id;
	}
}

The check for equality is added only for performance:

	if (o == this) return true;

In the equals it's not required a null check, because this is automatically managed by instanceof:

	if(o == null) return false; // Not required