User Tools

    To create and edit articles, please register and log-in

Main Menu

Main menu
Click categories to expand


A-Z listingplugin-autotooltip__plain plugin-autotooltip_bigA-Z listing

This is an alphabetical index of all content pages.


Other categories

Utilities

Contact
Register

Also see

Importance Ratings
News
Legal
Donate/Sponsor
Curator's rationale


Wikenigma supports:


Feeds etc
rss / xml feed
sitemap file
A-Z listing (archived)


Auto-Translate Site
Indexed under : Mathematics

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

The Scholz conjecture

The Scholz Conjecture relates the shortest length of an addition chain of mersene numbers to the shortest length of addition chains producing their exponents.

Stated formally as :

l(2n − 1) ≤ n − 1 + l(n),

where l(n) is the length of the shortest addition chain producing n.

Here, an addition chain is defined as a sequence of numbers, starting with 1, such that every number after the first can be expressed as a sum of two earlier numbers (which are allowed to both be equal). Its length is the number of sums needed to express all its numbers, which is one less than the length of the sequence of numbers (since there is no sum of previous numbers for the first number in the sequence, 1).“

Source : Wikipedia

Various 'weaker' versions of the conjecture have been proved. For example :

Brauer, Alfred (1939), "On addition chains" Bulletin of the American Mathematical Society, 45 (10): 736–739,

Agama,Theophilus (2022). "On the shortest addition chain of numbers of special forms" arXiv, mathematics, general mathematics, Mar. 2022.

Example chains have also been extensively investigated by computational methods. See: Clift, Neill Michael (2011). "Calculating optimal addition chains". Computing. 91 (3): 265–284.

But the full conjecture, as stated above, remains unproved.


    Share this page :

Dear reader : Do you have any suggestions for the site's content?

Ideas for new topics, and suggested additions / corrections for old ones, are always welcome.

If you have skills or interests in a particular field, and have suggestions for Wikenigma, get in touch !


Or, if you'd like to become a regular contributor . . . request a login password. Registered users can edit the entire content of the site, and also create new pages.

( The 'Notes for contributors' section in the main menu has further information and guidelines etc.)

Automatic Translation

You are currently viewing an auto-translated version of Wikenigma

Please be aware that no automatic translation engines are 100% accurate, and so the auto-translated content will very probably feature errors and omissions.

Nevertheless, Wikenigma hopes that the translated content will help to attract a wider global audience.

Show another (random) article

DOKUWIKI IMPLEMENTATION DESIGN BY UNIV.ORG.UK MAY 2022