MathDB

CMI 2017 #3

Source: CMI 2017

April 26, 2018

CMIChennai Mathematical InstitutemathCS2017calculuspolynomial

Problem Statement

Let

p(x)

be a polynomial of degree strictly less than

100

and such that it does not have

(x^3-x)

as a factor. If

\frac{d^{100}}{dx^{100}}\bigg(\frac{p(x)}{x^3-x}\bigg)=\frac{f(x)}{g(x)}

for some polynomials

f(x)

and

g(x)

then find the smallest possible degree of

f(x)