Hilbert-Waring Theorem/Particular Cases/7
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Particular Case of the Hilbert-Waring Theorem: $k = 7$
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 $k = 7$ is:
Every positive integer can be expressed as the sum of at most $143$ positive seventh powers.
That is:
- $g \left({7}\right) = 143$
Proof
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