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*(2*n*− 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":

**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)