Problem

Source: Girls in Mathematics Tournament 2021 p3 (Brazil) / Torneio Meninas na Matematica (TM^2) / Brazil EGMO TST 2022 #3

Tags: number theory, divisible, sum of digits



A natural number is called chaotigal if it and its successor both have the sum of their digits divisible by $2021$. How many digits are in the smallest chaotigal number?