MathNet 2023-part-02 — 191 problems (EN–VI) Question 148

Find the remainder when $1 \times 2 \times 3 \times 4 + 2 \times 3 \times 4 \times 5 + \dots + 2023 \times 2024 \times 2025 \times 2026$ is divided by $1000$.