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a^m has last digit 6 and the sum of the other digits is 3?

Source: Lithuania TST 2014 p4

September 28, 2020
number theoryLast digitsum of digits

Problem Statement

(a) Is there a natural number nn such that the number 2n2^n has last digit 66 and the sum of the other digits is 22? b) Are there natural numbers aa and m≥3m\ge 3 such that the number ama^m has last digit 66 and the sum of the other digits is 3?
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