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Regional Olympiad - FBH 2017 Grade 11 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

September 19, 2018
Divisorsnumber theorynumber of divisors

Problem Statement

It is given positive integer NN. Let d1d_1, d2d_2,...,dnd_n be its divisors and let aia_i be number of divisors of did_i, i=1,2,...ni=1,2,...n. Prove that (a1+a2+...+an)2=a13+a23+...+an3(a_1+a_2+...+a_n)^2={a_1}^3+{a_2}^3+...+{a_n}^3
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