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f(1)+f(2)+...+f(2005) if f(a) is largest integer <= \sqrt[4]{a}

Source: Chile Finals 2005 L2 p4

October 3, 2022
number theoryalgebra

Problem Statement

Let f(a)f(a) be the largest integer less than or equal to the fourth root of " aa". Calculate f(1)+f(2)+...+f(2005).f(1)+f(2)+...+f(2005).
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