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Hi. Do we have to mind putting the article in front of nouns when using either the word 'either' or the word 'neither'?

Let us pretend there is a pen and pencil and you need one of them to write and you need either of them.

A: I need either pen (a pen?) or pencil (a pencil).

Let us pretend there is a pen and pencil but you already have a pencil. You don't need either of them.

A: I don't need neither pen (a pen?) nor pencil (a pencil?).

Also, did I write my question on top of the post after the 'Hi' correctly?
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Hi. Do we have to put the article in front of nouns when using either the word 'either' or the word 'neither'?-- Usually, yes.

A: I need either a pen or (a) pencil.

A: I need neither a pen nor (a) pencil,
Comments  
Thank you. I looked at the dictionary and I think it said that the words 'either' and 'neither' are determiners. I the the words 'determiners' and 'articles' are pretty much the same and I also believe the words 'a' and 'an' are articles.