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CSMO 2017 Grade 10 Problem 3

Source: Chinese Southeast Mathematical Olympiad

August 1, 2017
modular arithmeticnumber theory

Problem Statement

For any positive integer nn, let DnD_n denote the set of all positive divisors of nn, and let fi(n)f_i(n) denote the size of the set Fi(n)={a∈Dn∣a≡i(mod4)}F_i(n) = \{a \in D_n | a \equiv i \pmod{4} \} where i=1,2i = 1, 2. Determine the smallest positive integer mm such that 2f1(m)−f2(m)=20172f_1(m) - f_2(m) = 2017.
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