MathDB

2

Part of 2018 Poland - Second Round

Problems(1)

Divisors inequality

Source: 69 Polish MO 2018 Second Round - Problem 2

4/28/2018
Let nn be a positive integer, which gives remainder 44 of dividing by 88. Numbers 1=k1<k2<...<km=n1 = k_1 < k_2 < ... < k_m = n are all positive diivisors of nn. Show that if i∈{1,2,...,m−1}i \in \{ 1, 2, ..., m - 1 \} isn't divisible by 33, then ki+1≤2kik_{i + 1} \le 2k_{i}.
number theorycombinatoricsDivisorsPolandinequalities