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2 trinomials with same value at x=1234

Source: Russian Regional Olympiad 2010 11.7

August 24, 2024
algebratrinomial

Problem Statement

Integers a,b,ca,b,c are such that the values of the trinomials bx2+cx+abx^2+cx+a and cx2+ax+bcx^2+ax+b at x=1234x=1234 coincide. Can the first trinomial at x=1x = 1 take the value 20092009?
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