Solving congruences

U ovom završnom radu upoznat ćemo se s načinima i metodama rješavanja različitih tipova kongruencija. Na početku ćemo definirati sustave ostataka koji su nam vrlo bitni pri određivanju rješenja kongruencija. Nadalje, prikazat ćemo postupak rješavanja linearnih kongruencija, polinomijalnih kongruencija sa složenim modulima te polinomijalnih kongruencija s prostim potenciranim modulima. Navest ćemo te na primjerima primjenjivati Kineski teorem o ostatcima koji nam je koristan pri rješavanju sustava linearnih kongruencija. Također ćemo navesti i kroz primjere prikazati primjenu Fermatovog i Lagrangeovog teorema koji su nam korisni pri rješavanju kongruencija s prostim modulima.In this final paper we will introduce ways and methods of solving different types of congruences. At the beginning we will define the residue systems, which are very important in obtaining solutions of congruences. Furthermore, the procedure of solving linear congruences, polynomial congruences with composite moduli and polynomial congruences with prime power moduli will be shown. We will cite The Chinese remainder theorem, which is very useful in solving simultaneous linear congruences, and apply it to examples. We will also cite and through examples present the applications of Fermat’s and Lagrange’s theorem, which are useful in solving congruences with prime moduli