Erdős–Tetali theorem

In additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive bases of every order. More specifically, it states that for every fixed integer ${\displaystyle h\geq 2}$, there exists a subset of the natural numbers ${\displaystyle {\mathcal {B}}\subseteq \mathbb {N} }$ satisfying

where ${\displaystyle r_{{\mathcal {B}},h}(n)}$ denotes the number of ways that a natural number n can be expressed as the sum of h elements of B.

The theorem is named after Paul Erdős and Prasad V. Tetali, who published it in 1990.