MMO 250 Moscow MO 1953 1953 digits on a circle, no divisible by 27
Source:
August 9, 2019
number theorycombinatoricsdivisible
Problem Statement
Somebody wrote digits on a circle. The -digit number obtained by reading these figures clockwise, beginning at a certain point, is divisible by . Prove that if one begins reading the figures at any other place, one gets another -digit number also divisible by .