| Abstract [eng] |
The main focus of this thesis lies in the multiplicative dependence of two integers shifted by an algebraic number. A particular motivation for this topic comes from the paper of P. Drungilas and A. Dubickas. We looked into the main ideas of the proof of the above-mentioned conjecture and discussed some other important results. We successfully examined the multiplicative dependence of two integers shifted by an algebraic number, which is not an algebraic integer. We also looked into the multiplicative dependence of two integers shifted by a square algebraic number and formulated a conjecture based on empirical evidence. Finally, we found infinitely many positive integers such that any two of those integers shifted by an algebraic number from a particular infinite class are multiplicatively independent. |
