MathDB
2012-2013 Winter OMO #39

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January 16, 2013
Online Math Opennumber theoryrelatively primegreatest common divisor

Problem Statement

Find the number of 8-digit base-6 positive integers (a1a2a3a4a5a6a7a8)6(a_1a_2a_3a_4a_5a_6a_7a_8)_6 (with leading zeros permitted) such that (a1a2…a8)6∣(ai+1ai+2…ai+8)6(a_1a_2\ldots a_8)_6\mid(a_{i+1}a_{i+2}\ldots a_{i+8})_6 for i=1,2,…,7i=1,2,\ldots,7, where indices are taken modulo 88 (so a9=a1a_9=a_1, a10=a2a_{10}=a_2, and so on).
Victor Wang
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