VTMO 2026 - Grade 7 - Final - SET 9 - Self-study Question 2

Arrange the integers from 1 to 2015 in any order. Subtract 1 from the first, 2 from the second, and so on, subtracting 2015 from the last. Let $P$ be the product of the resulting 2015 numbers. Prove that $P^2+2P$ is divisible by 8.