MathDB

084

Part of 1941 Moscow Mathematical Olympiad

Problems(1)

MMO 084 Moscow MO 1941 factoring in 2 integer polynomials

Source:

7/18/2019
a) Find an integer aa for which (x−a)(x−10)+1(x - a)(x - 10) + 1 factors in the product (x+b)(x+c)(x + b)(x + c) with integers bb and cc.
b) Find nonzero and nonequal integers a,b,ca, b, c so that x(x−a)(x−b)(x−c)+1x(x - a)(x - b)(x - c) + 1 factors into the product of two polynomials with integer coefficients.
polynomialFactoringalgebra