THE ADDITIVE COMPLETION OF KTH-POWERS

Let k ≥ 2 be an integer. For fixed N, we consider a set AN of non-negative integers such that for all integer n ≤ N, n can be written as n = a + bk, a ∈ AN, b a positive integer. We are interested in a lower bound for the number of elements of AN. Improving a result of R. Balasubramanian (J. Number Theory29, 1988, 10-12), we prove the following theorem: [formula]. © 1993 Academic Press Inc.