改进了H.涉及2阶（mod u）II的Mueller
Improvement of an estimate of H. Mueller involving the order of 2(mod u) II
摘要：
设m>=1是任意固定整数，N_m（x）表示使得模u的2阶不能被m整除的奇数u<=x的个数.当m是素数时，H.穆勒，随后锐化成一个渐近估计由本作者。穆勒在他的回合延长作者的结果的情况下，其中m是一个总理的权力和界限的情况下，m是不是一个总理的权力。本文导出了N_m（x）的一个渐近解，它对所有整数m都成立.如果不是因为某个丢番图方程有非平凡解的事实，这个渐近式很容易从穆勒的方法中推导出来。确定了该方程的所有解。我们也推广到其他底数比2。对于这些数字的一个非常稀疏的集合，穆勒的方法确实有效。
英文摘要：
Let m>=1 be an arbitrary fixed integer and let N_m(x) count the number of odd integers u<=x such that the order of 2 modulo u is not divisible by m. In case m is prime estimates for N_m(x) were given by H. Mueller that were subsequently sharpened into an asymptotic estimate by the present author. Mueller on his turn extended the author's result to the case where m is a prime power and gave bounds in the case m is not a prime power. Here an asymptotic for N_m(x) is derived that is valid for all integers m. This asymptotic would easily have followed from Mueller's approach were it not for the fact that a certain Diophantine equation has non-trivial solutions. All solutions of this equation are determined. We also generalize to other base numbers than 2. For a very sparse set of these numbers Mueller's approach does work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
