Question 147
We say that an integer sequence $\{a_1, a_2, \dots\}$ is good if for some function $f: \mathbb{Z}^+ \to \mathbb{Z}^+$ and all positive integers $i, j, n$
$$
a_i \equiv a_j \pmod{n} \Leftrightarrow i \equiv j \pmod{f(n)}
$$
Find all good sequences.
$$
a_i \equiv a_j \pmod{n} \Leftrightarrow i \equiv j \pmod{f(n)}
$$
Find all good sequences.