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n monic trinomials x^2-a_i x + b_i - All-Russian MO 2006 Regional (R4) 10.4

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September 27, 2024
algebrapolynomialtrinomial

Problem Statement

Given n>1n > 1 monic square trinomials x2−a1x+b1x^2 - a_1x + b_1,......, x2−anx+bnx^2-a_nx + b_n, and all 2n2n numbers are a1a_1,......, ana_n, b1b_1,......, bnb_n are different. Can it happen that each of the numbers a1a_1,......, ana_n, b1b_1,......, $b_n is the root of one of these trinomials?
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