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Source: 2005 China Second Round Olympiad

September 2, 2014
functionfloor functiongeometrygeometric transformationalgebra unsolvedalgebra

Problem Statement

For each positive integer, define a function f(n)={0,if n is the square of an integer⌊1{n}⌋,if n is not the square of an integer. f(n)=\begin{cases}0, &\text{if n is the square of an integer}\\ \\ \left\lfloor\frac{1}{\{\sqrt{n}\}}\right\rfloor, &\text{if n is not the square of an integer}\end{cases}. Find the value of ∑k=1200f(k)\sum_{k=1}^{200} f(k).
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