Hilbert-Waring Theorem/Particular Cases/6

Particular Case of the Hilbert-Waring Theorem: $k = 6$

The Hilbert-Waring Theorem states that:


For each $k \in \Z: k \ge 2$, there exists a positive integer $\map g k$ such that every positive integer can be expressed as a sum of at most $\map g k$ positive $k$th powers.


The case where $k = 6$ is:

Every positive integer can be expressed as the sum of at most $73$ positive sixth powers.

That is:

$\map g 6 = 73$


Proof


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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $73$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $73$
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