olymmath

PL-OM 2018 Problem 2

    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} .

    Dataset text AI-MO AoPS. Quoted with source.

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