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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 622.10041

**Autor: ** Erdös, Paul; Nathanson, Melvyn B.

**Title: ** Problems and results on minimal bases in additive number theory. (In English)

**Source: ** Number theory, Semin. New York 1984/85, Lect. Notes Math. 1240, 87-96 (1987).

**Review: ** [For the entire collection see Zbl 605.00005.]

Let h in **N**. A set A of nonnegative integers such that every sufficiently large integer is representable as the sum of h elements of A is called an asymptotic basis of order h. In this paper a number of old and new problems concerning the classical asymptotic bases (squares, higher powers, primes) as well as the general properties of asymptotic bases are discussed. Of special interest are questions about the existence of minimal bases A, i.e. A is an asymptotic basis of order h but no proper subset of A has this property.

**Reviewer: ** J.Zöllner

**Classif.: ** * 11B13 Additive bases

11B83 Special sequences of integers and polynomials

11P05 Waring's problem and variants

11P05 Waring's problem and variants

11P32 Additive questions involving primes

00A07 Problem books

**Keywords: ** sums of squares; sums of higher powers; sums of primes; asymptotic basis; problems; minimal bases

**Citations: ** Zbl 605.00005

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