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Problem 593

AMC 12 late, AIME early

Number theory Difficulty 5.0 Find the answer

7.1. Provide an example of a natural number that is a multiple of 2020, such that the sum of its digits is also a multiple of 2020.

Your answer

Official solution

Solution: For example, the number 20202020...2020, where the fragment 2020 repeats 505 times, fits. Such a number is obviously divisible by 2020, and the sum of its digits is $505 \times 4=2020$ .

Criteria: Any correct answer with or without verification - 7 points.

Correctly conceived example, but with a calculation error (for example, 2020 repeats 500 times) - 3 points.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.