This is an example of how ReSharper writes a Gethashcode() function for you:.
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If the Gethashcode() is equal, it is not necessary for them to be the same;
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Also often a object will NEVER be used in a collection that depends on Gethashcode().
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So the cost of implementing Gethashcode() is often not worth it,
or it is not possible.
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It's actually very hard to implement Gethashcode() correctly because,
in addition to the rules Marc already mentioned, the hash code should not change during the lifetime of an object.
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If someone puts your object in a collection that calls Gethashcode() and you have overrided Equals() without also making Gethashcode()
behave in a correct way, that person may spend days tracking down the problem.