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What are the confusions & resolution(if any) , those have occurred in the history of the Theory of Numbers?

I have come across :

Is 1 a prime number:counter proof?

Is 0 a natural number: no general agreement about whether to include 0 in the set of natural numbers?

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    @Rahul Yes, that was what puzzled me. Units are excluded from being prime or irreducible mainly for *convenience*, even though they do satisfy the respective divisibility properties.2012-08-04

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I think it took a while to figure out what should pass for the ring of integers in a number field.