10.5

Part of 2009 All-Russian Olympiad Regional Round

Problems(1)

Last digit of a power of 2

Source: Problem 5 of Russian Regional Olympiad 2009 Grade 10

Positive integer

m

is such that the sum of decimal digits of

2^m

equals 8. Can the last digit of

2^m

be equal 6?
(Author: V. Senderov)

number theory proposednumber theory