I try to explaine my problem and I hope do not disturb or annoy;
I know that number theory is very vast but essentially it is divided into two parts:
analytic number theory and algebraic number theory;
My questions are: what are the main tool used for working on it, the main topic that one can study and the main active reaserch areas in this two sectors?
what are their applications to study the property of the integers?
what is in general number theory today?
Thanks to all for your valuable answers!