MathDB

Let

k \in \mathbb{Z}^+

and set

n=2^k+1.

Prove that

n

is a prime number if and only if the following holds: there is a permutation

a_{1},\ldots,a_{n-1}

of the numbers

1,2, \ldots, n-1

and a sequence of integers

g_{1},\ldots,g_{n-1},

such that

n

divides

g^{a_i}_i - a_{i+1}

for every

i \in \{1,2,\ldots,n-1\},

where we set

a_n = a_1.

Proposed by Vasily Astakhov, Russia

Problem Statement