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Remainder in the divison by a quadratic polynomial

Source: 1st Brazilian MO, 1979, Problem 2 (from Kalva backup)

December 23, 2017
quadraticspolynomialpolynomial divisionBrazilian Math OlympiadalgebraBrazilian Math Olympiad 1979

Problem Statement

The remainder on dividing the polynomial p(x)p(x) by x2−(a+b)x+abx^2 - (a+b)x + ab (where a≠ba \not = b) is mx+nmx + n. Find the coefficients m,nm, n in terms of a,ba, b. Find m,nm, n for the case p(x)=x200p(x) = x^{200} divided by x2−x−2x^2 - x - 2 and show that they are integral.
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