Each implementation of Equals must fulfil the following requirements:

• Reflexive: An object must equal itself.x.Equals(x) returns true.
• Symmetric: There is no difference if I compare x to y or y to x - the result is the same. x.Equals(y) returns the same value as y.Equals(x).
• Transitive: If one object is equal to another object and this one is equal to a third one, the first has to be equal to the third.if (x.Equals(y) && y.Equals(z)) returns true, then x.Equals(z) returns true.
• Consistent: If you compare an object to another multiple times, the result is always the same.Successive invocations of x.Equals(y) return the same value as long as the objects referenced by x and y are not modified.
• Comparison to null: No object is equal to null.x.Equals(null) returns false.

Implementations of GetHashCode:

• Compatible with Equals: If two objects are equal (meaning that Equals returns true), then GetHashCode must return the same value for each of them.
• Large range: If two objects are not equal (Equals says false), there should be a high probability their hash codes are distinct. Perfect hashing is often not possible as there is a limited number of values to choose from.
• Cheap: It should be inexpensive to calculate the hash code in all cases.

See: Guidelines for Overloading Equals() and Operator ==

Writing a good GetHashCode override

Default Equals behavior.

Override Equals and GetHashCode on custom types

Equals and GetHashCode in IEqualityComparator