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Divisors inequality

Source: 69 Polish MO 2018 Second Round - Problem 2

April 28, 2018

number theorycombinatoricsDivisorsPolandinequalities

Problem Statement

Let

n

be a positive integer, which gives remainder

4

of dividing by

8

. Numbers

1 = k_1 < k_2 < ... < k_m = n

are all positive diivisors of

n

. Show that if

i \in \{ 1, 2, ..., m - 1 \}

isn't divisible by

3

, then

k_{i + 1} \le 2k_{i}