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I.S.I. B.Math.(Hons.) Admission test : 2010 Problem 9

Source:

April 11, 2012
algebrapolynomial

Problem Statement

Let f(x)f(x) be a polynomial with integer co-efficients. Assume that 33 divides the value f(n)f(n) for each integer nn. Prove that when f(x)f(x) is divided by x3āˆ’xx^3-x , the remainder is of the form 3r(x)3r(x) where r(x)r(x) is a polynomial with integer coefficients.
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