Bonjour, I've never made extensive researches in number theory, scared to lost myself, so... I would like to ask you something : Could you help me to find some sources(or anything else) about the distribution and the interactions/properties[...] of elements for any structures(if that does exist, but I'm pretty sure it exists, even if...).
I'll give you an exemple : Imagine you are working on the set of natural numbers, you would like to find the "informations" about the intrinsic properties/rules of that set (for instance, the distribution of numbers of the form $ak+b$ (it's only an example), the behavior when you apply a transformation compared to an abstract object, when you add $a$ and $b$ : be able to say if a+b will be even or odd (without doing the operation) and so on...).
I've try to be the more comprehensive that i could, but that stays a little bit confusing I guess. Sorry... If you want any kind of informations/precision, I'll be there.
Thanks.
Ps: I hope that you could have understand me without any trouble, because I'm a young french student (16 years old).
Unfortunately, in mathematics, there is no general encyclopedia or database for the known mathematical structures and terms. You could look for numbers, for algebraic structures and for combinatorial structures.
Search for example in:
Google
Google Books
Online Encyclopedia of Integer Sequences (https://oeis.org)
Encyclopedia of Combinatorial Structures (http://ecs.inria.fr)
Wolfram mathworld (http://mathworld.wolfram.com)
Wikipedia
Wikipedia: list of mathematical