Schnirelmann density Totally Explained

Everything about Schnirelmann Density totally explained

In mathematics, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is. It is named after Russian mathematician L.G. Schnirelmann, who was the first to study it.

Definition

The Schnirelmann density of a set of natural numbers is defined as follows

Definition. Let $A subseteq N$ . We write $A(n)$ to denote $#(A cap ^k) > 0$ .

We have thus established the general solution to Waring's Problem:

Corollary. (Hilbert, 1909) For all $k$ there exists $N$ , depending only on $k$ , such that every positive integer $n$ can be expressed as the sum of at most $N$ many $k$ -th powers.

Goldbach's conjecture

See Goldbach's conjecture.

Further Information

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