>>>   Can you count how many topics of number theory there are here?
>>> http://en.wikipedia.org/wiki/List_of_number_theory_topics
> 
>> OK, so I forgot Diophantine equations (which are admittedly a pretty 
>> large area).
> 
>   And combinatorics, fractions, finite and infinite sequences and series,
> L-functions, etc...

It's news to me that combinatorics is related to number theory.

A fraction is merely a pair of coprime numbers. (So, prime numbers and 
divisibility again then...)

My number theory book doesn't mention anything about series, finite or not.

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