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MathNet 2021 — Part 07 Question 82

Math Olympiad Vault · MathNet 2021 — Part 07

Question 82

Do there exist two polynomials $P$ and $Q$ with integer coefficient such that
i) both $P$ and $Q$ have a coefficient with absolute value bigger than $2021$,
ii) all coefficients of $P \cdot Q$ by absolute value are at most $1$.