Overriding Equality Operators

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I've implemented a class that overloads the == and != operators.

This seems to work fine; however, I get the warning 'type' defines operator == or operator != but does not override Object.Equals(object o).

Okay, so I implemented Equals. But now I get the warning 'type' defines operator == or operator != but does not override Object.GetHashCode().

Does this end at some point? Or have I wandered into a never-ending trail of requirements just because I want to overload == and !=?

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