Fractional Part Function | Floors & Fractional Parts

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We present techniques for dealing with problems involving the floor and the fractional part function, focusing on the fractional part function. The techniques are varied and apply to many different problems including quadratic equations in the fractional part and floor function, equations that sums involving the fractional part function, and even integrals.

The key idea is to represent things in terms of integers.

#FractionalPartFunction #FloorFunction #OlympiadProblems

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@18:58 if n<=x<(n+1) then -(n+1)<(-x)<=(-n). Let f(x) be the floor of x and f(x)=n while f(-x)=-(n+1)=-n-1. Taking difference, -f(x)-f(-x)=-n-(-n-1)=1

zh
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I found your channel recently and I just loved it ❤️❤️❤️

divyanshukumar
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Really great video.especially the integral

yoav