2022/10/25 by Tall, Amadou
#11Y16 #11Y55 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2210.13812
It is known that the Scholz conjecture on addition chains is true for all integers n with ℓ(2n) = ℓ(n)+1. There exists infinitely many integers with ℓ(2n) ≤ ℓ(n) and we don't know if the conjecture still holds for them. The conjecture is also proven to hold for integers n with v(n) ≤ 5 and for infinitely many integers with v(n)=6. There is no specific results on integers with v(n)=7. In \citethurber, an infinite list of integers satisfying ℓ(n) = ℓ(2n) and v(n) = 7 is given. In this paper, we prove that the conjecture holds for all of them.