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n-digit numbers M , N - All-Russian MO 1998 Regional (R4) 8.1

Source:

September 17, 2024
number theoryDigits

Problem Statement

Are there nn-digit numbers M and N such that all digits MM are even, all NN digits are odd, every digit from 00 to 99 occurs in decimal notation M or N at least once, and MM is divisible by NN?
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