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Number of even and odd divisors

Source: Kürschák 1999, problem 1

July 15, 2014
number theory unsolvednumber theory

Problem Statement

For any positive integer mm, denote by di(m)d_i(m) the number of positive divisors of mm that are congruent to ii modulo 22. Prove that if nn is a positive integer, then ∣∑k=1n(d0(k)−d1(k))∣≤n.\left|\sum_{k=1}^n \left(d_0(k)-d_1(k)\right)\right|\le n.
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