39

Part of 2013 Online Math Open Problems

Problems(1)

2012-2013 Winter OMO #39

Source:

Find the number of 8-digit base-6 positive integers

(a_1a_2a_3a_4a_5a_6a_7a_8)_6

(with leading zeros permitted) such that

(a_1a_2\ldots a_8)_6\mid(a_{i+1}a_{i+2}\ldots a_{i+8})_6

i=1,2,\ldots,7

, where indices are taken modulo

8

a_9=a_1

a_{10}=a_2

, and so on).
Victor Wang

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