Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
gptkb:Diophantine_equations
additive problems |
| gptkbp:concerns |
representation of natural numbers as sums of powers
|
| gptkbp:example |
Every natural number is the sum of four squares (k=2, s=4)
Every natural number is the sum of nineteen fourth powers (k=4, s=19) Every natural number is the sum of nine cubes (k=3, s=9) |
| gptkbp:field |
number theory
|
| gptkbp:formedBy |
1770
|
| gptkbp:generalizes |
gptkb:Lagrange's_four-square_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Waring's problem
|
| gptkbp:namedAfter |
gptkb:Edward_Waring
|
| gptkbp:notableAchievement |
Exact values of s(k) known for small k
Hilbert proved existence of s for all k |
| gptkbp:relatedTo |
gptkb:Hilbert–Waring_theorem
additive number theory |
| gptkbp:solvedBy |
gptkb:David_Hilbert
1909 |
| gptkbp:type |
whether for every k ≥ 2 there exists a positive integer s such that every natural number is the sum of at most s k-th powers
|
| gptkbp:bfsParent |
gptkb:Edward_Waring
|
| gptkbp:bfsLayer |
5
|