Euler's sum of powers conjecture (1769): at least n nth powers are needed to sum to an nth power.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Assessment
Renown 4/5
Euler's own conjecture, standing 197 years.
Attackability 4/5
A single quintuple of integers, found by direct machine search in 1966; the founding example of the genre.
- finite witness
- 5/5
- oracle cost
- 5/5
- freshness
- 2/5
- seedability
- 2/5
Confirmed resolution
counterexample by L. J. Lander and T. R. Parkin on .
27^5 + 84^5 + 110^5 + 133^5 = 144^5, found by direct search on a CDC 6600; the announcement is one of the shortest papers ever published.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
Confirmed
This entry no longer accepts claims or resolution reports.