Primitive Roots and Their Applications

Tema ovoga rada su primitivni korijeni, indeksi i njihove primjene. Najprije ćemo uvesti bitne rezultate teorije brojeva koji će nam kasnije u radu pomoći definirati pojmove primitivnih korijena i indeksa te primijeniti to na različitim primjerima i vidjeti kako se oni računaju. Na kraju ćemo vidjeti neke poznatije probleme kao što su Artinova hipoteza, Diffie-Hellmanov problem te Shanksov algoritam.In this paper, we will deal with primitive roots, indices, and their applications. Firstly, we will introduce some important results in theory of numbers which will help us later in the paper to define terms of primitive roots and indices. Further, we will apply it to different examples and see how they are calculated. Finally, we will see some well-known problems related to primitive roots and indices such as the Artin’s hypothesis, the Diffie-Hellman problem and the Shanks algorithm