Waring's problem
Problema de Waring
- Date
- 1770 · confidence high
- Place
- University of Cambridge, Cambridge, United Kingdom
- Credited to
- Edward Waring
- Field
- Knowledge & symbols
What was discovered
Waring, Lucasian professor at Cambridge, conjectured that for every exponent k there is a number s such that every positive integer can be written as a sum of at most s k-th powers (e.g. 4 squares, 9 cubes, or 19 fourth powers). David Hilbert proved it in 1909.
What it led to
- The Hilbert–Waring theorem (1909)
- Research in analytic number theory (Hardy, Littlewood, Vinogradov)
Built on
- Lagrange's four-square theorem1770
- Bachet's conjecture on the sum of four squares, proved by Lagrange (1770)