• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Representation of Natural Numbers by Units

Student: Gubanov Sergei

Supervisor: Andrey Levin

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Final Grade: 8

Year of Graduation: 2020

We consider representations of natural numbers by units, using only addition, multiplication and parentheses. It is known that for a certain positive integer $n$ the least number of units needed to represent it in such a way (we denote it by $f(n)$) ranges between $3 \log_3 n$ and $3 \log_2 n$ with an optimal lower bound, that is attained infinitely many times by powers of three. But it's still unknown whether $f(n) \sim 3 \log_3 n$ or not. We try to approach to this by considering powers of two.

Full text (added June 1, 2020)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses