Cube (algebra)
In integers
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==In integers== |
==In integers== |
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{{see also|Cube-free integer}} |
{{More citations needed|section|date=April 2026}}{{see also|Cube-free integer}} |
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A '''cube number''', or a '''perfect cube''', or sometimes just a '''cube''', is a number which is the cube of an [[integer]]. |
A '''cube number''', or a '''perfect cube''', or sometimes just a '''cube''', is a number which is the cube of an [[integer]]. |
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The non-negative perfect cubes up to 603 are {{OEIS|id=A000578}}: |
The non-negative perfect cubes up to 603 are {{OEIS|id=A000578}}: |
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===Waring's problem for cubes=== |
===Waring's problem for cubes=== |
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{{main|Waring's problem}} |
{{main|Waring's problem}} |
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Every positive integer can be written as the sum of nine (or fewer) positive cubes. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine positive cubes: |
Every positive integer can be written as the sum of nine (or fewer) positive cubes. This upper limit of nine cubes cannot be reduced because, for example, 23 cannot be written as the sum of fewer than nine positive cubes: |
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