{"id":"repeated-division-terminates","text":"The `while n: n //= k` loop terminates in O(log_k(n)) iterations for k >= 2 because integer division by k >= 2 strictly decreases a positive n toward zero.","truth_value":"IN","source":"entries/2026/06/06/sum-of-digits-in-base-k-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"repeated-division-terminates","truth_value":"IN","reason":"premise"}]}}