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MMO 241 Moscow MO 1953 polynomial x^{200}y^{200}+1 cannot be f(x) g(y)

Source:

August 9, 2019

algebrapolynomialfactor

Problem Statement

Prove that the polynomial

x^{200} y^{200} +1

cannot be represented in the form

f(x)g(y)

, where

f

and

g

are polynomials of only

x

and

y

, respectively.