O nekim Eulerovim doprinosima u teoriji brojeva

Leonhard Euler (1707.-1783.) najproduktivniji je matematičar svih vremena. Dao je ogroman doprinos svakom matematičkom području svog vremena, ali i mnogim drugim znanostima kao što su geografija, fizika, teorija glazbe, ... Postavio je temelje nekim matematičkim granama, a smatra se da je posebnu "virtuoznost'' pokazao baveći se teorijom brojeva. U radu ćemo opisati samo neke njegove doprinose elementarnoj teoriji brojeva, primjerice dokaz Malog Fermatovog teorema, Velikog Fermatovog teorema za \(n=3\) i Teorema o dva kvadrata te mnoge zaključke vezane uz djeljivost prirodnih brojeva, Legendreov simbol i Pellovu jednadžbu.Leonhard Euler (1707. - 1783.) is the most productive mathematician of all time. He made enormous contributions to every mathematical branch of his time as well as to many other fields of science such as geography, physics, music theory,… He laid the foundations for some mathematical branches, however, number theory is considered the branch where his “virtuosity” was most evident. This paper describes just some of his contributions to elementary number theory, such as the proof of Fermat’s little theorem, Fermat’s last theorem for \(n = 3\) and his Theorem on the sum of two squares as well as many conclusions related to the divisibility of natural numbers, the Legendre symbol and Pell’s equation