Integer Divisor Results/Every Integer Divides Itself

Theorem

Let $n \in \Z$, i.e. let $n$ be an integer.

Then:

$n \backslash n$

That is, $n$ divides itself.

Proof

As the set of integers form an integral domain, the concept divides is fully applicable to the integers.

Therefore this result follows directly from Every Element Divisor of Itself.

$\blacksquare$

Sources

• C.R.J. Clapham: Introduction to Abstract Algebra (1969)... (previous)... (next): $\S 3.10$
• George E. Andrews: Number Theory (1971): $\S 2.2$: Example $2.2$
• Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 22$