MathDB
f(x) = x^{m+n} -x^{m+1} -x+1, g(x) = x^{m+n} +x^{n+1} -x+1

Source: Romania IMO TST 1993 2.2

February 17, 2020
algebrapolynomialdivisor

Problem Statement

For coprime integers m>n>1m > n > 1 consider the polynomials f(x)=xm+n−xm+1−x+1f(x) = x^{m+n} -x^{m+1} -x+1 and g(x)=xm+n+xn+1−x+1g(x) = x^{m+n} +x^{n+1} -x+1. If ff and gg have a common divisor of degree greater than 11, find this divisor.
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