Question 21
Prove that, for every positive integer $n$ which ends in the digit 5,
$$
20^n + 15^n + 8^n + 6^n
$$
is divisible by 2009.
$$
20^n + 15^n + 8^n + 6^n
$$
is divisible by 2009.
MathNet 2026 — Part 05 Question 21
Math Olympiad Vault · MathNet 2026 — Part 05