MathDB

Let

p{}

be a prime number. There are

p{}

integers

a_0,\ldots,a_{p-1}

around a circle. In one move, it is allowed to select some integer

k{}

and replace the existing numbers via the operation

a_i\mapsto a_i-a_{i+k}

where indices are taken modulo

p{}.

Find all pairs of natural numbers

(m, n)

with

n>1

such that for any initial set of

p{}

numbers, after performing any

m{}

moves, the resulting

p{}

numbers will all be divisible by

n{}.

Proposed by P. Kozhevnikov

Problem Statement