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5-degree polynomial, divisible by x^2-x+1, coefficients in1-8

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 3.5

September 25, 2021
algebrapolynomialdivisible

Problem Statement

Determine the number of polynomials of degree 55 with different coefficients in the set {1,2,3,4,5,6,7,8}\{1, 2, 3, 4, 5, 6, 7, 8\} such that they are divisible by x2āˆ’x+1x^2-x + 1. Justify your answer.
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