20

Part of 1990 IMO Shortlist

Problems(1)

In the decimal system with at most four different digits

Source: IMO ShortList 1990, Problem 20 (POL 3)

Prove that every integer

k

greater than 1 has a multiple that is less than

k^4

and can be written in the decimal system with at most four different digits.

pigeonhole principlenumber theorydecimal representationDivisibilitymultipleIMO ShortlistDigits