Hilbert-Waring Theorem/Particular Cases/5
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Particular Case of the Hilbert-Waring Theorem: $k = 5$
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 $\map g k$ $k$th powers.
The case where $k = 5$ is:
Every positive integer can be expressed as the sum of at most $37$ positive fifth powers.
That is:
- $g \left({5}\right) = 37$
Proof
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Also see
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $37$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $37$