Fundamental assumption about number theory: divisibility

Some interesting questions arose in my mind. The Mathematics we have built to date depend on the fundamental assumptions we make in the very beginning. For example, if we consider Number Theory - more precisely divisibility (see [1], page 24) - we come upon the following statement:

An integer $d$ is said to divide $n$ or be a divisor of $n$ if there exists an integer $e$ such that $n=de$.

I am wondering:

1. Is this an axiom?


2. Is this a fact of life arising from nature, or was this invented?



3. Can a different Mathematics be built if we change this statement?

Bonus points for anyone who can point me to literature that covers topics such as:

1. Fundamental nature of Number Theory (or in general, Mathematics)


2. Possibility of other variants of Number Theory (or in general, Mathematics)

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[1] Kenneth S. Williams, 2010. Number Theory in the Spirit of Liouville. Cambridge University Press.

Answer

It is just a definition of a concept, a notion that mathematicians stumbled across. So, they just gave it a name (divisor). They could also have called the concept "Peter" or "Flabber" or whatever. The concept was not invented but found/discovered. This is also true for many other mathematical concepts such as groups, for example. Even though groups do not appear in there pure form in nature, their concept can be transferred to many instances in reality (for example, in quantum mechanics).
By simply assigning a different name to the word divisor we do not get some "different Mathematics" since we are only dealing with a definition and not with an axiom. If your statement was indeed an axiom, we could very well end up with some different mathematics if we changed it. A good example for this is the parallel postulate in geometry. If you replace the parallel postulate of Euclidean Geometry with

For any given line $R$ and point $P$ not on $R$, in the plane containing both line $R$ and point $P$ there are at least two distinct lines through $P$ that do not intersect $R$. (taken from: Wikipedia),

then you will come to Hyperbolic geometry which is indeed very different from Euclidean geometry.

Concerning your last question about possible variants of number theory, you might find analytic number theory interesting, which brings together methods from number theory and mathematical analysis such as complex analysis.