exist exactly 3^{k-1} natural numbers n with the 4 following properties
Source: Austrian - Polish 1996 APMC
May 3, 2020
number theorydividesdivisibleDigits
Problem Statement
Let be a positive integer. Prove that there exist exactly natural numbers with the following properties:
(i) has exactly digits (in decimal representation),
(ii) all the digits of are odd,
(iii) is divisible by ,
(iv) the number has odd digits