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Find a,b,m,n such that x^n+ax+b divides x^m+ax+b

Source: Romanian IMO Team Selection Test TST 2003, problem 7

September 24, 2005
algebrapolynomialVietatrigonometryalgebra proposed

Problem Statement

Find all integers a,b,m,na,b,m,n, with m>n>1m>n>1, for which the polynomial f(X)=Xn+aX+bf(X)=X^n+aX+b divides the polynomial g(X)=Xm+aX+bg(X)=X^m+aX+b. Laurentiu Panaitopol
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