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(a+1)/2-digit number of 2s and 0s

Source: 2020 China North Mathematical Olympiad Advanced Level P5

August 4, 2020

number theoryDigitsmultiple

Problem Statement

Find all positive integers

a

so that for any

\left \lfloor \frac{a+1}{2} \right \rfloor

-digit number that is composed of only digits

0

and

2

(where

0

cannot be the first digit) is not a multiple of

a