olymmath

Putnam 2021 A6

  • Session A

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 a product of two nonconstant polynomials with integer coefficients. Does it follow that P(2)P(2) is a composite integer?

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Manjul Bhargava, Kiran Kedlaya and Lenny Ng

The terms of the source let olymmath link to this solution but not copy it. Read the solution (Kedlaya Putnam archive).

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