本文研究了和素数有关的方程组和不等式组。通过更细致的指数和估计，我们改进了以前的结果。
In this paper we study systems of Diophantine inequalities and equations with prime Numbers. We improve previous results by more delicate estimates of exponential sums.
给出了所有准素子群的正规化子有素数幂指数的有限群的幂零长的界。
The bounds of nilpotent lengths of finite groups with normalizers of primary subgroups having prime power indices are obtained.
另一方面，如果你想要一个大的您要进行因式分解的数字，将参数作为(素数，指数)对的序列传递。
If, on the other hand, you want the value of the totient for some large number for which you have the factorization, pass the argument as sequence of (prime, exponent) pairs.
你正在测试的指数产生一个梅森素数的概率是1/143369。
The chance that the exponent you are testing will yield a Mersenne prime is about 1 in 143369.
指数是无效的，当它比数组的下限或大于或等于其包含的元素数量降低。
Index is invalid when it's lower than array's lower bound or greater or equal than number of elements it contains.
指数是无效的，当它比数组的下限或大于或等于其包含的元素数量降低。
Index is invalid when it's lower than array's lower bound or greater or equal than number of elements it contains.
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