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composition of quadratic polynomials

Source: All-Russian olympiad 1995, Grade 9, First Day, Problem 3

October 20, 2013
quadraticsalgebrapolynomialsymmetryfunctioncomplex numbersalgebra proposed

Problem Statement

Can the equation f(g(h(x)))=0f(g(h(x))) = 0, where ff, gg, hh are quadratic polynomials, have the solutions 1,2,3,4,5,6,7,81, 2, 3, 4, 5, 6, 7, 8?
S. Tokarev
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