Effective Algorithms for Finding the Remainder of Multi-Digit Numbers

In this paper, the theoretical foundations of the developed methods for finding the remains of multi-digit numbers and the Mersenne number in a binary number system are given, the use of which allows reducing the time complexity. The numerical experiments of the time characteristics of program implementations of the proposed approaches and the classical method are given. The scheme of the algorithm for finding the remainder of the multi-digit number and the multi-digit Mersenne number is given.

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