Control Systems and Computers, N2, 2022, Article 8
https://doi.org/10.15407/csc.2022.02.070
Control Systems and Computers, 2022, Issue 2 (298), pp. 70-76
UDC 511
V.K. Bilyk, Ph.D. Eng. Sciences, Senior Research Associate, V.M.Glushkov Institute of Cybernetics of the NAS of Ukraine,Acad. Glushkov Ave., 40, Kyiv, 03187, Ukraine, bilykvk@gmail.com
Simple and Visual Algorithm for Factorizing Integer Numbers
An iterative algorithm for decomposing an integer composite number C into prime factors X1 and X2 is proposed in which the properties of Vieta’s theorem are used for the reduced quadratic equations X2+B·X·C = 0, when the first approximation in iterative computation is taken equal to the square root of the composite number C, then is С, and B is equal to the rounded up to a larger integer from the number С, that is, B = C. In this case, the calculations are carried out by linearly increasing the approximations by one.
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Keywords: factorization of numbers, prime and composite numbers.
- Ishmukhametov, Sh.T., 2011. Methods of factorization of natural numbers: textbook. Kazan: Kazan University, 190 p. (In Russian).
- Vinogradov, I.M., 1981. Fundamentals of number theory. M.: Nauka. 176 p (In Russian).
- Shor, P., 1997. “Polynomial – Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer”. SIAM Jour.Comp., Vol. 26, N 5, pp. 1484-1509.
https://doi.org/10.1137/S0097539795293172 - Semotyuk, M.V., 2013. “On the analytical method of factorization of composite numbers”.Computers zasobi, festoon and systems. N 12, pp. C. 5– (In Ukrainian).
- Gusev, V.A., Mordkovich, A.G., 1988. Mathematics: Ref. materials. M.: Education, 416 p. (In Russian).
Received 30. 03.2021
