Fundamental Theorem of Arithmetic

Tema ovog završnog rada bila je osnovni teorem aritmetike. U prvom dijelu rada upoznajemo se s osnovnim strukturama brojeva koje su nam potrebne za daljnju razradu osnovnog teorema aritmetike. Također, potreban nam je pojam djeljivosti u skupu cijelih bojeva te prosti brojevi koje uvodimo neposredno nakon podjele brojeva na prirodne i cijele. Zatim, uz pomoć prostih brojeva navodimo osnovni teorem aritmetike i njegov dokaz. Teorem je vrlo koristan rezultat u matematici. Primjenjuje se u mnogim područjima teorije brojeva. Veoma je važan u raznim primjenama kongruencija, kao i u primjeni metoda za šifriranje i dešifriranje poruka kojima se bavi znanstvena disciplina kriptografija.The theme of this nal work was the fundamental theorem of arithmetic. In the rst part of the paper, we will get acquainted with the basic structure of numbers that we need to further elaborate the fundamental theorem of arithmetic. Also, we need the notion of divisibility in the set of whole numbers and the prime numbers that we introduce immediately after the division of numbers into the natural and the whole. Then, with the help of prime numbers, we state the fundamental theorem of arithmetic and its proof. The theorem is a very useful result in mathematics. Applies to many areas of the theory of numbers. It is very important in various applications of congruence, as well as in the application of methods for encryption and decryption of messages dealing with scientic discipline cryptography