Ivasiev S. Methods and Computational Tools for Solving the Problems in Theory of Numbers for Rademacher's and Krestenson's Basis.

Object of research - process of hardware and multi-processing numbers of specialized computer systems using theoretical - numerical basis Rademacher - Krestenson; subject of investigation - methods, algorithms and hardware tools reduce the time and difficulties in processing multi numbers on the basis of theoretical - numerical basis Rademacher - Krestenson; the analytical expressions for characteristics of complexity, which are characterized by a lower temporal complexity in comparison with the existing, enhanced functional capabilities and reduce the amount of required memory procedure while maintaining big numbers have been obtained in this thesis on the basis of the developed methods of calculations in the Rademacher's and Krestenson's Basis and big numbers factorization algorithm, big prime numbers compact coding, finding residues of big numbers, modular multiplication, determining quadratic residue of a number by module, method of determining the vicinity for solving the problems of factorization for the computer system.