ÖMO 2000 Problem 5

Find all pairs of integers $(m, n)$ such that $\left| (m^2 + 2000m+ 999999)- (3n^3 + 9n^2 + 27n) \right|= 1.$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.