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5-degree polynomial such that (x-1)^3| P(x)+1 and (x+1)^3| P(x)-1

Source: Polish second round 1994 p1

January 19, 2020

algebrapolynomialpolynomial division

Problem Statement

Find all real polynomials

P(x)

of degree

5

such that

(x-1)^3| P(x)+1

and

(x+1)^3| P(x)-1