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Show that $a_{2m}=10a_{2m-1}

Source: Moldova TST 2004

March 8, 2023
combinatoricsnumber theory

Problem Statement

Let aka_k be the number of nonnegative integers n n with the properties: a) n∈[0,10k)n\in[0, 10^k) has exactly k k digits, such that he zeroes on the first positions of n n are included in the decimal writting. b) the digits of n n can be permutated such that the new number is divisible by 11.11. Show that a2m=10a2m−1a_{2m}=10a_{2m-1} for every m∈N.m\in\mathbb{N}.
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