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Divisors of n are distinct mod m

Source: China TSTST Test 2 Day 1 Q1

March 13, 2017
number theoryDivisorsmodular arithmetic

Problem Statement

Let nn be a positive integer. Let DnD_n be the set of all divisors of nn and let f(n)f(n) denote the smallest natural mm such that the elements of DnD_n are pairwise distinct in mod mm. Show that there exists a natural NN such that for all n≥Nn \geq N, one has f(n)≤n0.01f(n) \leq n^{0.01}.
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