{"id":"divisor-game-parity-invariant","text":"Alice wins the Divisor Game if and only if n is even; the proof relies on Alice always subtracting 1 from even n to hand Bob an odd number, maintaining the invariant. The solution is O(1).","truth_value":"IN","source":"entries/2026/06/06/divisor-game-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"divisor-game-parity-invariant","truth_value":"IN","reason":"premise"}]}}