Existence of some Large Number
Source: INAMO 2023 P4 (OSN 2023)
August 29, 2023
number theoryDigitsNT constructionIndonesiaIndonesia MO
Problem Statement
Determine whether or not there exists a natural number which satisfies the following three criteria:
1. is divisible by , but not by ,
2. only has three different digits, and none of them are zero,
3. Exactly 99.9% of the digits of are odd.