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The Largest Integer Not the Sum of Distinct 8th Powers
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Michael J. Wiener

20 Hennepin St.

Nepean, ON K2J 3Z4

Canada

**Abstract:**

The largest integer that is not the sum of one or more distinct squares
is 128 and is called the threshold of completeness for the set of
squares. A natural extension is to consider positive cubes and higher
powers. Previous research solved this problem for powers up to 7. Our
contribution is the threshold of completeness for 8th powers as well as
lower bounds for powers from 9 to 16. We also describe the mathematical
methods we used to speed up computations. Using 200,000 computer cores,
our methods could find the threshold of completeness for 9th powers in
about a month, and for 10th powers in about a year.

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(Concerned with sequences
A001661
A010060.)

Received January 21 2023; revised versions received February 4 2023; May 16 2023; June 1
2023.
Published in *Journal of Integer Sequences*,
June 6 2023.

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