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Last digit of a power of 8

Source: Problem 6 of Russian Regional Olympiad 2009 Grade 9

September 19, 2011
number theory proposednumber theory

Problem Statement

Positive integer mm is such that the sum of decimal digits of 8m8^m equals 8. Can the last digit of 8m8^m be equal 6?
(Author: V. Senderov)
(compare with http://www.artofproblemsolving.com/Forum/viewtopic.php?f=57&t=431860)