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CSMO Grade 11 Problem 4

Source: China Southeast Mathematical Olympiad

August 1, 2017
number theoryDivisorsCalculate

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=0,1,2,3i = 0, 1, 2, 3. Determine the smallest positive integer mm such that f0(m)+f1(m)−f2(m)−f3(m)=2017f_0(m) + f_1(m) - f_2(m) - f_3(m) = 2017.
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