MathDB

Given a prime

p

and positive integer

k

, an integer

n

with

0 \le n < p

is called a

(p, k)

-Hofstadterian residue if there exists an infinite sequence of integers

n_0, n_1, n_2, \ldots

such that

n_0 \equiv n

and

n_{i + 1}^k \equiv n_i \pmod{p}

for all integers

i \ge 0

. If

f(p, k)

is the number of

(p, k)

-Hofstadterian residues, then compute

\displaystyle \sum_{k = 1}^{2016} f(2017, k)

.
Proposed by Ashwin Sah

Problem Statement