MathNet 2019-part-05 — 184 problems (EN–VI) Question 149

100 distinct positive integers are arranged in a circle. Vasya divided each number by its clockwise neighbor with remainder, and he obtained only two distinct remainders. Petya divided each number by its counter-clockwise neighbor with remainder. Prove that Petya obtained 100 distinct remainders.
(N. Agakhanov, S. Berlov)