论文标题
Scholz猜想加法链上的猜想是无限的许多整数，$ \ ell（2n）= \ ell（n）$
The Scholz conjecture on addition chain is true for infinitely many integers with $\ell(2n)= \ell(n)$
论文作者
论文摘要
众所周知，对于所有整数$ n $，带有$ \ ell（2n）= \ ell（n）+1 $的所有整数$ n $都是如此。存在$ \ ell（2n）\ leq \ ell（n）$的无限整数，我们不知道猜想是否仍然适合它们。该猜想还被证明可以为整数$ n $提供，其中$ v（n）\ leq 5 $，对于无限的许多整数（$ v（n）= 6 $）。 $ v（n）= 7 $的整数没有具体的结果。在\ cite {thurber}中，给出了满足$ \ ell（n）= \ ell（2n）$和$ v（n）= 7 $的无限整数列表。在本文中，我们证明了猜想对所有人都有。
It is known that the Scholz conjecture on addition chains is true for all integers $n$ with $\ell(2n) = \ell(n)+1$. There exists infinitely many integers with $\ell(2n) \leq \ell(n)$ and we don't know if the conjecture still holds for them. The conjecture is also proven to hold for integers $n$ with $v(n) \leq 5$ and for infinitely many integers with $v(n)=6$. There is no specific results on integers with $v(n)=7$. In \cite{thurber}, an infinite list of integers satisfying $\ell(n) = \ell(2n)$ and $v(n) = 7$ is given. In this paper, we prove that the conjecture holds for all of them.
