MathDB

Let

c

and

n > c

be positive integers. Mary's teacher writes

n

positive integers on a blackboard. Is it true that for all

n

and

c

Mary can always label the numbers written by the teacher by

a_1,\ldots, a_n

in such an order that the cyclic product

(a_1-a_2)\cdot(a_2-a_3)\cdots(a_{n-1}-a_n)\cdot(a_n-a_1)

would be congruent to either

0

c

modulo

n

Problem Statement