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Putnam 2021 A6

Source:

December 5, 2021
PutnamPutnam 2021

Problem Statement

Let P(x)P(x) be a polynomial whose coefficients are all either 00 or 11. Suppose that P(x)P(x) can be written as the product of two nonconstant polynomials with integer coefficients. Does it follow that P(2)P(2) is a composite integer?
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