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Greece Junior National Olympiad 1977-78 problem 3

Source:

August 10, 2015

number theory

Problem Statement

Let

k

be a prime, such as

k\neq 2, 5

, prove that between the first

k

terms of the sequens

1, 11, 111, 1111,....,1111....1

, where the last term have

k

ones, is divisible by

k

.

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