MathDB

To commemorate the

43rd

anniversary of the restoration of mathematics competitions, a mathematics enthusiast arranges the first

2021

integers

1,2,\dots,2021

into a sequence

\{a_n\}

in a certain order, so that the sum of any consecutive

43

items in the sequence is a multiple of

43

. (1) If the sequence of numbers is connected end to end into a circle, prove that the sum of any consecutive

43

items on the circle is also a multiple of

43

; (2) Determine the number of sequences

\{a_n\}

that meets the conditions of the question.

Problem Statement