Finding the order of the automorphism group of the abelian group of order 8.

If you are familiar with finite fields, it's easiest to see this by viewing $G=\mathbb{Z}_2\times \mathbb{Z}_2 \times \mathbb{Z}_2$ as a vector space of dimension $3$ over $\mathbb{F}_2$. In this way, we see that the automorphism group of $G$ is $GL_3(\mathbb{F}_2)$, the group of $3 \times 3$ invertible matrices over $\mathbb{F}_2$. By counting the ways to make three linearly independent vectors, we see that $$|\operatorname{Aut}(G)|=(2^3-1)(2^3-2)(2^3-2^2)=168.$$ If you don't know what a finite field is, this isn't as easy. Finite fields are easy to understand if they have prime order, though - just add and multiply the numbers $0,\ldots, p-1$ modulo $p$. (As it turns out, finite fields always have prime power order, but things get more complicated when the power is greater than $1$.)

Why does the infinite prisoners and hats puzzle require the axiom of choice?

Problem about Ricci flow

Isomorphism between $E_8$ lattice and lattice defined by Extended Hamming Code

Which is the better approximation to $e$?

Why do we use open intervals in most proofs and definitions?

Is it possible that a clock's three hands divide the clock face into 3 equal parts?

What is the relationship between $(u\times v)\times w$ and $u\times(v\times w)$?

Show that there are infinitely many solutions of distinct natural numbers $m,n$ such that $n^3+m^2\mid m^3+n^2$

Stirling numbers combinatorial proof

Classify all groups containing isomorphic copy of $\mathbb{Z}$ of index $2$.

Where did Descartes write, "With me everything turns into mathematics."

Integral of $e^{-x^2}\cos(x^2)$ using residues