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multiple of n with digits only 8,9 (I Soros Olympiad 1994-95 R1 9.10 10.10 11.9)

Source:

July 31, 2021
number theorymultipleDigits

Problem Statement

For which natural nn there exists a natural number multiple of nn, whose decimal notation consists only of the digits 88 and 99 (possibly only from numbers 88 or only from numbers 99)?
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