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0161 number theory 1st edition Round 6 p1

Source:

May 9, 2021
number theory1st edition

Problem Statement

Let a,ma, m be two positive integers, a≠10ka \ne 10^k, for all non-negative integers kk and d1,d2,...,dmd_1, d_2, ... , d_m random decimal1^1 digits with d1>0d_1 > 0. Prove that there exists some positive integer nn for which the representation in the decimal base of the number ana^n begins with the digits d1,d2,...,dmd_1, d_2, ... , d_m in this order.
1^1 lesser or equal with 99
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