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 $1$.
Source: 2021 Saudi Arabia BMO TST 1.1
Tags: algebra, polynomial
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 $1$.