Tidbits

The Fibonacci sequence was originally used to model the growth of (idealized) rabbit populations (Wikipedia):

A newly born breeding pair of rabbits are put in a field; each breeding pair mates at the age of one month, and at the end of their second month they always produce another pair of rabbits. How many pairs of rabbits are there after a year?

There exists a complex sequence $(a_n)_n$ such that $\sum_{n \ge 0} a_n^k$ converges if and only if $k$ is prime.

More generally, for any fixed subset $A \subseteq \mathbb{Z}^+$, there exists a complex sequence $(a_n)_n$ such that $\sum_{n \ge 0} a_n^k$ converges if and only if $k \in A$. (Math Stack Exchange)

If $a(b+1)(ab+1)$ is a perfect square, then $(b+1)$ divides $a(ab+1)$.

(I originally posed this as a conjecture on Math Stack Exchange based on computational evidence, and user Mastrem provided a proof using a clever descent argument.)

In Go, the following is not an error:

type A struct { Field string }
type B struct { Field int }
type C struct { A; B }

even though C embeds A and B, both of which declare a field called Field.

If $f : \mathbb{Z}^\infty \to \mathbb{Z}$ is an additive function that vanishes on all sequences of the form $(1, 0, 0, \dots)$, $(0, 1, 0, \dots)$, $(0, 0, 1, \dots)$, and so on, then $f$ is the zero function. (Math Stack Exchange)

If this seems obvious, note that the statement is false for $f : \mathbb{Z}^\infty \to \mathbb{Q}$ under AC.