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MMO 084 Moscow MO 1941 factoring in 2 integer polynomials

Source:

July 18, 2019

polynomialFactoringalgebra

Problem Statement

a) Find an integer

a

for which

(x - a)(x - 10) + 1

factors in the product

(x + b)(x + c)

with integers

b

and

c

.
b) Find nonzero and nonequal integers

a, b, c

so that

x(x - a)(x - b)(x - c) + 1

factors into the product of two polynomials with integer coefficients.