| Abstract [eng] |
In this master thesis it is written about theorems, corollaries, theory of linear forms in logarithms and how the forms are usefully applied in number theory, especially Diophantine equations, mostly exponential. Some of the theory uses facts about transcendental, algebraic numbers. Most Diophantine equations in this thesis are exponential, because after the theorems that directly describe linear forms in logarithms it is written about other theorems that instead of logarithms have exponents with bases. The fact that, e.g., $\exp(b\log a)=a^b$, where $a>0$, $a,b\in\mathbb R$, is used. For applications of linear forms in logarithms the bounds of Diophantine equation solutions are found, existence of the bounds is shown, the fact that there exists a finite number of solutions is proven, all solutions are found, etc. A lot of attention is given to the Catalan conjecture, which is now a theorem. |
