MathDB

Let

a_k

be the number of nonnegative integers

n

with the properties: a)

n\in[0, 10^k)

has exactly

k

digits, such that he zeroes on the first positions of

n

are included in the decimal writting. b) the digits of

n

can be permutated such that the new number is divisible by

11.

Show that

a_{2m}=10a_{2m-1}

for every

m\in\mathbb{N}.

12