The tags elementary-number-theory and number-theory have been recently mentioned in this question: There are 1,732 questions tagged both elementary-number-theory and number-theory However, in that question these two tags serve only as an illustration of a more general issue. In this post I'd like to concentrate on the question whether we can agree on the content of these two tags.
I should say that, in my opinion, the distinction between these two tags should not be based on difficulty, but rather on the content of the questions. (Not every question about divisibility is easy. Not every question about analytic number theory is difficult.) Of course, even a question which is about rather simple concept may require advanced tools. In such case tag might be added later. See Retagging after an answer is given.
When I am not sure whether question belongs to some tag, I usually consult the tag-wiki and the tag-excerpt. However, in this case, this does not help much:
Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.
Questions on elementary, or "classic", number theory: congruences, greatest common divisor identities, divisibility, etc.
Questions on more advanced topics of number theory. Consider first if (elementary-number-theory) might be a more appropriate tag before adding this tag.
For questions on congruences, linear Diophantine equations, greatest common divisors, etc., please use the elementary-number-theory tag.
If you compare the situation with elementary-set-theory and set-theory, you will see that the tag-wikis contain a list of topics which belong under the tag in question. This contrasts with rather subjective wording more advanced topics in the tag-info for (number-theory).
- How do you decide what belongs in elementary-number-theory and what belongs in number-theory? Is there some relatively simple rule of thumb?
- Could we perhaps be able to make a list of topics which belong to elementary-number-theory and list of areas which fall under number-theory?
- If we are able to reach some agreement about the content of the two tags, it would be useful to improve the tag-info for these two tags.