Additive basis

In additive number theory, an additive basis is a set of natural numbers with the property that, for some finite number , every natural number can be expressed as a sum of or fewer elements of . That is, the sumset of copies of consists of all natural numbers. The order or degree of an additive basis is the number . When the context of additive number theory is clear, an additive basis may simply be called a basis. An asymptotic additive basis is a set for which all but finitely many natural numbers can be expressed as a sum of or fewer elements of .

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