Two number-theoretic applied problems
UDC: 517.935.2
DOI: 10.33285/2782-604X-2023-7(600)-51-57
Authors:
DMITRIEV NIKOLAY N.1,
OSETINSKIY NIKOLAY I.
1
1 National University of Oil and Gas "Gubkin University", Moscow, Russia
Keywords: graph, discrete linear system, vertex, edge, recurrent equation, cycle, digit
Annotation:
Two problems are considered. The first one is related to graph theory, the second one – to number theory. The first problem can be used in solving some transportation problems of oil and gas, the second one – in the applied cryptography. Both problems are also of independent scientific interest. In addition to solving in particular cases, for the first problem, the asymptotics of the behavior of the main value as a function of the natural argument is found. In the second problem, the cyclicity of the function of the sum of the lth powers of the digits of a natural number is proved.
Bibliography:
1. Mezhdunarodnaya Matematicheskaya Olimpiada. – URL: https://www.imo-official.org/
2. International Mathematical Olympiad. Problems and Solutions 1959–2009. – Zadacha iz mezhdunarodnoy matematicheskoy olimpiady (1964 god). – URL: https://hengsokha.files.wordpress.com/2011/06/imo-problem-solution-1959-2009.pdf
3. Williams E.S. Further Generalizations of Happy Numbers. – 2016. – URL: http://sections.maa.org/epadel/awards/studentpaper/winners/2016_Williams.pdf
4. Voropaeva N.V., Sobolev V.A., Shchepakina E.A. Analiz i dekompozitsiya diskretnykh dinamicheskikh sistem: ucheb. posobie. – Samara: Samarskiy un-t, 2014. – 88 s.
5. Yumagulov M.G. Vvedenie v teoriyu dinamicheskikh sistem. – SPb.: Lan', 2015. – 272 s.
6. Elementy diskretnoy matematiki v zadachakh / A.A. Glibichuk, A.B. Daynyak, D.G. Il'inskiy [i dr.]. – M.: MTsMNO, 2016. – 176 s.
7. Shteyngauz G. Sto zadach. – M.: Nauka, 1976. – 168 s.
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