Random article ( of 1062 ) Latest updates

User Tools

Site Tools


content:mathematics:halls_conjecture

Wikenigma - an Encyclopedia of Unknowns Wikenigma - an Encyclopedia of the Unknown

Hall's conjecture

In 1970, American mathematician Marshall Hall Jr. conjectured that :

$${\displaystyle |y^{2}-x^{3}| >C{\sqrt {|x|}}.}$$

Or, in language form : For any ε > 0, there exists a constant c(ε) > 0 such that if x and y are positive integers satisfying x3 − y2 6 ≠ 0, then |x3 − y2| > c(ε)x1/2−ε (ref.)

It remains an open question.

Technical details here (arXiv.org)


Show another (random) article

Suggestions for corrections and ideas for articles are welcomed : Get in touch!


Further resources :

Do NOT follow this link or you will be banned from the site!

DOKUWIKI IMPLEMENTATION DESIGN BY UNIV.ORG.UK MAY 2024