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 100.
(b) Give an example of such a progression with 72 terms.
(c) Prove that the number of terms in any such progression does not exceed 72.(V. Bugaenko and Tarasov, Moscow) number theoryArithmetic ProgressionDigits