MathDB

Let

\mathbb{Z}_{>0}

denote the set of positive integers. For any positive integer

k

, a function

f: \mathbb{Z}_{>0} \to \mathbb{Z}_{>0}

is called

k

-good if

\gcd(f(m) + n, f(n) + m) \le k

for all

m \neq n

. Find all

k

such that there exists a

k

-good function.
Proposed by James Rickards, Canada

N7