TOT 319 1991 Autumn A S6 arithmetical progression eithout 9s
Source:
June 9, 2024
number theoryArithmetic ProgressionDigits
Problem Statement
An arithmetical progression (whose difference is not equal to zero) consists of natural numbers without any nines in its decimal notation.
(a) Prove that the number of its terms is less than .
(b) Give an example of such a progression with terms.
(c) Prove that the number of terms in any such progression does not exceed .(V. Bugaenko and Tarasov, Moscow)