MathNet 2026 — Part 07 Question 54

Let $a, b, c, d$ be integers. Prove that for any positive integer $n$, at least $\lfloor \frac{n}{4} \rfloor$ positive integers $m \le n$ are such that $m^5 + d m^4 + c m^3 + b m^2 + 2021 m + a$ is not a perfect square.