Scholz Conjecture

In mathematics, the Scholz conjecture sometimes called the Scholz–Brauer conjecture or the Brauer–Scholz conjecture (named after A. Scholz and Alfred T. Brauer), is a conjecture from 1937 stating that

l(2n − 1) ≤ n − 1 + l(n) where l(n) is the length of the shortest addition chain producing n. N. Clift checked this by computer for n ≤ 46.

As an example, l(5) = 3 (since 1 + 1 = 2, 2 + 2 = 4, 4 + 1 = 5, and there is no shorter chain) and l(31) = 7 (since 1 + 1 = 2, 2 + 1 = 3, 3 + 3 = 6, 6 + 6 = 12, 12 + 12 = 24, 24 + 6 = 30, 30 + 1 = 31, and there is no shorter chain), so

l(25−1) = 5 − 1 + l(5).

Other articles related to "scholz conjecture, scholz, conjecture":

Addition Chain - Scholz Conjecture
... The Scholz conjecture (sometimes called the Scholz–Brauer or Brauer–Scholz conjecture), named after A ... Scholz and Alfred T ... Brauer), is a conjecture from 1937 stating that l(2n − 1) ≤ n − 1 + l(n) ...

Famous quotes containing the word conjecture:

    What these perplexities of my uncle Toby were,—’tis impossible for you to guess;Mif you could,—I should blush ... as an author; inasmuch as I set no small store by myself upon this very account, that my reader has never yet been able to guess at any thing. And ... if I thought you was able to form the least ... conjecture to yourself, of what was to come in the next page,—I would tear it out of my book.
    Laurence Sterne (1713–1768)