Geodesic
A Lower Bound for the Scholz-Brauer Problem
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 675-683

Voir la notice de l'article provenant de la source Cambridge University Press

In (6)Scholz asked if the inequality 1.1 held for all positive integers q, where l(n)is the number of multiplications required to raise xto the nth power (a precise definition of l(n)in terms of addition chains is given in § 2). Soon afterwards, Brauer (2) showed, among other things, that l(n) ∼(log n)/(log2). This suggests the problem of Calculating 1.2 It can be deduced from (2) that θ≦ 1. If θ <1, (1.1) follows immediately for infinitely many q.My main result,Theorem 5 of § 4, merely shows that θ is slightly larger than 1⁄3.Actually, I know of no case where (1.1) is not in fact an equality; a tedious calculation verifies this for 1 ≦ q≦ 8. 
Stolarsky, Kenneth B. A Lower Bound for the Scholz-Brauer Problem. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 675-683. doi: 10.4153/CJM-1969-077-x
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