Zvanje: | redoviti profesor u trajnom zvanju |
Lokacija: | 301 |
Telefon: | 01 460 5780 |
E-mail: | |
Osobna stranica na Webu: | https://web.math.pmf.unizg.hr/~duje/ |
Zavod/služba: | Zavod za algebru i teoriju brojeva |
Godina diplomiranja: | 1990. |
Godina magistriranja: | 1993. |
Godina doktoriranja: | 1996. |
Na zavodu od: | 1996. |
prijediplomski
diplomski
srijeda 14-16
An elliptic curve over Q(u) with torsion Z/4Z and rank 6
Extensions of a Diophantine triple by adjoining smaller elements II
Diophantine m-tuples and Elliptic Curves
On power values of pyramidal numbers, II,
High-rank elliptic curves with given torsion group and some applications
Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields
Absolute root separation
Extensions of a Diophantine triple by adjoining smaller elements
Stjepan Bohniček (December 15, 1872 - March 14, 1956)
On elliptic curves induced by rational Diophantine quadruples
Triples, quadruples and quintuples which are D(n)- sets for several n's
D(n)-quintuples with square elements
Diophantine m-tuples in finite fields and modular forms
Number Theory
Elliptic curves with torsion groups Z/8Z and Z/2Z × Z/6Z
Lie Groups, Number Theory, and Vertex Algebras
Diophantine triples with largest two elements in common
Construction of high rank elliptic curves
Rational Diophantine sextuples containing two regular quadruples and one regular quintuple
Doubly regular Diophantine quadruples
Diophantine quadruples with the properties D(n1) and D(n2)
Strong rational Diophantine D(q)-triples
High rank elliptic curves induced by rational Diophantine triples
D(n)-sets with square elements
Rank zero elliptic curves induced by rational Diophantine triples
A Pellian equation with primes and applications to D(-1)-quadruples
Rational Diophantine sextuples with square denominators
Triples and quadruples which are D(n)-sets for several n's
On the largest element in D(n)-quadruples
Elliptic curves induced by Diophantine triples
Number Theory
Products of factorials which are powers,
On fundamental units of real quadratic fields of class number 1
Strong Eulerian triples
On Diophantine m-tuples and D(n)-sets
Triples which are D(n)-sets for several n's
Absolute real root separation
There are infinitely many rational Diophantine sextuples
On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields
There are infinitely many rational Diophantine sextuples
Polynomial root separation
Generiranje eliptičkih krivulja metodom kompleksnog množenja
Triples which are D(n)-sets for several n's
Root separation for reducible monic polynomials of odd degree
Kriptoanaliza RSA kriptosustava i njegovih inačica
Absolute real root separation
Primjena verižnih razlomaka u faktorizaciji i testiranju prostosti
More on Diophantine sextuples
On rational Diophantine sextuples
Protočna šifra RC4
Kvadratni ostaci i kvadratni korijeni u kriptografiji javnog ključa
Finiteness results for F-Diophantine sets
Diophantine quadruples in finite fields and modular forms
Rational Diophantine sextuples
Transcendentni brojevi
Diferencijalna kriptoanaliza
Number theory and cryptography
What is ... a Diophantine m-tuple?
There are infinitely many rational Diophantine sextuples
Number theory and cryptography
Elliptic curves with torsion group Z/6Z
NTRU kriptosustav
High-rank elliptic curves induced by Diophantine triples
Transpozicijske šifre ADFGX i ADFGVX
The rank and generators of Kihara's elliptic curve with torsion Z/4Z over Q(t)
The non-extensibility of D (-2k+ 1)-triples {;;1, k^ 2, k^ 2+ 2k-1};;
The 2nd Department of Mathematical, Physical and Chemical Sciences
Elliptic curves with torsion group Z/8Z or Z/2Z × Z/6Z
Načini djelovanja blokovnih šifri
Number theory and cryptography
On the torsion group of elliptic curves induced by D(4)-triples
Products of three factorials
Diophantine m-tuples with elements in arithmetic progressions
High rank elliptic curves with torsion Z/2Z × Z/4Z induced by Diophantine triples
Mordell-Weil groups of elliptic curves induced by Diophantine triples
Mordell-Weilove grupe i izogenije familija eliptičkih krivulja
Ranks of elliptic curves with prescribed torsion over number fields
On the high rank π/3 and 2π/3 - congruent number elliptic curves
Elliptic curves coming from Heron tringles
On quadratic twists of elliptic curves y^2=x(x-1)(x-lambda)
Root separation for integer polynomials
Root separation for integer polynomials
Some Diophantine properties of the sequence of S-units
Root separation for reducible integer polynomials
High rank elliptic curves with prescribed torsion group over quadratic fields
Diofantski problemi sa sumama djelitelja
Root separation for integer polynomials
On the existence of rational Diophantine quintuples with the property D(q)
Indefinite binary quadratic forms
Elliptic curves and triangles with three rational medians
Primjena eliptičkih krivulja u kriptografiji
Diffie-Hellmanov problem i problem diskretnog logaritma
Arithmetic progressions and Pellian equations
Sumsets being squares
Geometrijski pristup verižnim razlomcima
Protočne šifre
On the sum of two divisors of (n^2 + 1)/2
Konačna polja i polinomijalne kongruencije
Neki diofantski problemi nad imaginarnim kvadratnim poljima
Polynomial root separation and applications
On the rank of elliptic curves coming from rational Diophantine triples
On a conjecture regarding balancing with powers of Fibonacci numbers
On the size of sets in a polynomial variant of a problem of Diophantus
Root separation for reducible monic quartics
LLL algoritam i neke primjene u kriptografiji
On Hall's conjecture and related polynomial Pell's equation
On power values of pyramidal numbers
On a problem of Diophantus for rationals
On Hall's conjecture
On a variation of a congruence of Subbarao
Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization
Sigurnost na Internetu
Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization
On the size of sets whose elements have perfect power n-shifted products
Rangovi familija eliptičkih krivulja i primjene na diofantske probleme
Root separation for irreducible integer polynomials
Root separation for reducible monic quartics
On Hall's conjecture
Konvergente verižnih razlomaka i Newtonovi aproksimanti za kvadratne iracionalnosti
Solving a family of quartic Thue inequalities using continued fractions
Mordell-Weil groups of elliptic curves over number fields of small degree
Eliptičke krivulje velikog ranga nad kvadratnim poljima
Some Diophantine triples and quadruples for quadratic polynomials
Metode sita
Kvadratna polja i kvadratne forme
Kriptografija u Drugom svjetskom ratu
Sigurnost pametnih kartica u bankarstvu
Kompaktna reprezentacija cijelih kvadratnih brojeva i cjelobrojne točke na eliptičkim krivuljama
On the size of sets in a polynomial variant of a problem of Diophantus
Eliptičke krivulje nad konačnim poljima
Diophantine m-tuples
Polinomne varijantne Diofantova problema
High rank elliptic curves induced by Diophantine triples and congruent numbers
Elliptic curves
Diophantine quadruples in Z[√ -2]
On the rank of elliptic curves over Q(i) with torsion group Z/4Z × Z/4Z
Generiranje slučajnih brojeva
Elliptic equations
Strong Diophantine triples
A search for high rank congruent number elliptic curves
A variant of Wiener's attack on RSA
Rational Diophantine sextuples with mixed signs
Digitalni novac i digitalni čekovi
Savršeni brojevi
Mikroplaćanja
Visine u diofantskoj geometriji i posljedice abc-slutnje
Pametne kartice
Tehnologije za elektronsku trgovinu
Periodic Continued Fractions
Sigurnost sustava za mikroplaćanje
Distribution of Prime Numbers
Fermatovi brojevi
A variant of Wiener's attack on RSA
Mestre's Polynomial Method for Construction of High-rank Elliptic Curves
Primjena verižnih razlomaka u diofantskim aproksimacijama i kriptoanalizi
Autentifikacija digitalnim potpisom
Faktorizacija i ideali
Conjectures and results on the size and number of Diophantine tuples
Konveksni skupovi
Kriptosustavi s javnim ključem
A polynomial variant of a problem of Diophantus for pure powers
A variant of Wiener's attack on RSA with small secret exponent
RSA kriptosustav
Kriptografija javnog ključa
Strong Diophantine triples
On Worley's theorem in Diophantine approximations
A problem of Diophantus, Fermat and Euler and its generalizations
Kriptografija u školi
Cryptography in school
On arithmetic progressions on Pellian equations
Rješavanje kongruencija
Strong Diophantine triples
On the number of Diophantine m-tuples
Poligrafske supstitucijske šifre
Sigurnost bankarskih sustava
Infrastruktura javnih ključeva
Pellova jednadžba i Pitagorine trojke
On the family of Diophantine triples {;k-1, k+1, 16k^3-4k};
On Mordell-Weil groups of elliptic curves induced by Diophantine triples
On differences of two squares in some quadratic fields
Construction of high rank elliptic curves and related Diophantine problems
Decomposition of a recursive family of polynomials
Mordell-Weil groups of elliptic curves induced by Diophantine triples
Effective solution of the D(-1)-quadruple conjecture
Prikaz prostih brojeva pomoću kvadratnih formi
Euklidov algoritam
Distribucija kvadratnih ostataka
Kompleksni verižni razlomci
Primitivni korijeni i kvadratni ostaci
Načela oblikovanja modernih blokovnih kriptosustava
Sigurnost elektroničkog poslovanja
ENIGMA
Diophantine m-tuples and generalizations
Kriptografija
On a problem of Diophantus with polynomials
Digitalni vodeni žigovi
Steganografija: skrivanje podataka u sliku
Markovljev lanac
Diophantine m-tuples for linear polynomials. II. Equal degrees
Algebarski brojevi
On the D(-1)-quadruple conjecture
Algoritmi za množenje velikih brojeva
PGP - Pretty Good Privacy
Transpozicijske šifre
Methods for computing the rank of elliptic curves over Q(T)
Indecomposability of polynomials and related Diophantine equations
Kodovi za ispravljanje grešaka i McElieceov kriptosustav
Eliptičke krivulje i eliptičke funkcije
Sustavi pellovskih jednadžbi i problem proširenja nekih Diofantovih trojki
Diophantine Equations over Function Fields
High rank elliptic curves with prescribed torsion group
Moderne blokovne šifre
Problem diskretnog logaritma za eliptičke krivulje
Topološko-konveksne strukture
Square roots with many good approximants
On the indecomposabilty of polynomials
Diophantine m-tuples
Complete solution of a problem of Diophantus and Euler
Digitalni potpis i digitalni novac
Steganografija
Aritmetičke funkcije
Diophantine m-tuples for primes
Fibonacci numbers and sets with the property D(4)
Diophantine m-tuples and connections with eliptic curves
Rothov teorem
Diofantove četvorke u kvadratnim poljima
Asymptotic estimates for the number of Diophantine m-tuples
Sigurnost interneta i SSL protokol
Complete solution of the polynomial version of a problem of Diophantus
Povijest kriptografije
Monoalfabetske supstitucijske šifre
A family of quartic Thue inequalities
Mordell-Weilov teorem
Kriptosustav RC6
Application of LLL-algorithm in solving Diophantine equations
Vigenere Cipher
Newton's approximants and continued fractions
There are only finitely many Diophantine quintuples
On a problem of Diophantus and Euler
Bounds for the size of sets with the property D(n)
Continued fractions and RSA with small secret exponent
Shannonova teorija
Mathematical Basis of Public-Key Cryptography
Problem ruksaka i primjene u kriptografiji
On Diophantine quintuple conjecture
On a problem of Diophantus for higher powers
Construction of elliptic curves over Q with large rank
Kongruencije brojeva i polinoma
Mali Fermatov teorem i njegove posljedice
Verižni razlomci i primjene
Mordellov teorem
Kriptosustav DES
Statistička svojstva aritmetičkih funkcija
Continued fractions and RSA with small secret exponent
Ispitivanje prostosti
A polynomial variant of a problem of Diophantus and Euler
Mersenneovi i savršeni brojevi
Kneserov teorem
Dokazi nultog znanja
Kongruentni brojevi i eliptičke krivulje
Modularne funkcije i kompleksno množenje eliptičkih krivulja
On the size of Diophantine m-tuples
An example of elliptic curve over Q with rank equal to 15
Problem diskretnog logaritma
Diophantine m-tuples for linear polynomials
Diffie-Hellmanov protokol za distribuciju ključeva
Fibonaccijevi brojevi i zlatni rez
A parametric family of quartic Thue equations
An interesting property of a recurrence related to the Fibonacci sequence
An extension of an old problem of Diophantus and Euler. II
Construction of high-rank elliptic curves with non-trivial torsion group
Hash funkcije u kriptografiji
Polialfabetske šifre
Testovi prostosti
Diophantine m-tuples and elliptic curves
An absolute bound for the size of Diophantine m-tuples
Pierre de Fermat (1601.-1665.)
Newton's formula and continued fraction expansion of sqrt(d)
Diophantine equations for second order recursive sequences of polynomials
Dvoparametarska familija Thueovih jednadžbi četvrtog stupnja
A note on Diophantine quintuples
Irregular Diophantine m-tuples and elliptic curves of high rank
The Fibonacci numbers
Integer points on a family of elliptic curves
Diophantine triples and construction of high-rank elliptic curves over Q with three non-trivial 2-torsion points
A parametric family of elliptic curves
A proof of the Hoggatt-Bergum conjecture
An extension of an old problem of Diophantus and Euler
A bijective proof of Riordan's theorem on powers of Fibonacci numbers
Diophantine quadruples and quintuples modulo 4
A generalization of a theorem of Baker and Davenport
A problem of Diophantus and Pell numbers
A problem of Diophantus and Dickson's conjecture
Some estimates of the number of Diophantine quadruples
On the exceptional set in the problem of Diophantus and Davenport
Complete solution of a family of simultaneous Pellian equations
The problem of Diophantus and Davenport
On Diophantine quintuples
The problem of the extension of a parametric family of Diophantine triples
Complete solutions of certain families of simultaneous Pellian equations
The problem of Diophantus and Davenport for Gaussian integers
Generalized Fibonacci numbers and the problem of Diophantus
Some polynomial formulas for Diophantine quadruples
Mathematical competitions of high-school students
Diophantine quadruples for squares of Fibonacci and Lucas numbers
Generalization of a problem of Diophantus
A. Dujella: Diophantine m-tuples and Elliptic Curves, Springer, Cham, 2024.
A. Dujella: Number Theory, Školska knjiga, Zagreb, 2021.
A. Dujella, M. Kazalicki, M. Mikić and M. Szikszai, There are infinitely many rational Diophantine sextuples, Int. Math. Res. Not. IMRN 2017 (2) (2017), 490-508.
A. Dujella, There are only finitely many Diophantine quintuples, J. Reine Angew. Math. 566 (2004), 183-214.
A. Dujella and A. Petho, A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2), 49 (1998), 291-306.
Hrvatsko matematičko društvo
American Mathematical Society
The Fibonacci Association
International Association for Cryptologic Research
Diofantove m-torke, eliptičke krivulje, Thueove i indeksne jednadžbe (HRZZ), 2014-2018
Diofantske jednadžbe i eliptičke krivulje (MZOŠ), 2007-2013
1990-1993 pripravnik-postdiplomand, PMF-MO
1993-1997 asistent, PMF-MO
1997-2000 docent, PMF-MO
2000-2004 izvanredni profesor, PMF-MO
2004-2009 redoviti profesor, PMF-MO
2009- redoviti profesor u trajnom zvanju PMF-MO
pjevanje