Lajos Hajdu

University of Debrecen, Institute of Mathematics

room: M416
telephone: +36-52-512900/22800
e-mail: hajdul@science.unideb.hu
homepage: www.math.unideb.hu/~hajdul
 

Oktatás                 Teaching              Curriculum vitae                Publications                 Talks

Oktatás

    Gazdasági matematika I:

• Az előadás tematikája doc
• Feladatok a gyakorlatokhoz (szerzők: Losonczi László, Pap Gyula) pdf
• Előadáskövető jegyzet (szerzők: Losonczi László, Pap Gyula) pdf
• Előadáskövető fóliák (szerzők: Losonczi László, Pap Gyula) pdf
• Beadandó házi feladatok I. pdf
• Beadandó házi feladatok II. pdf
• A vizsgával kapcsolatos információk doc és minta feladatsor pdf

• Az előadás tematikája doc
• Feladatok a gyakorlatokhoz (szerzők: Losonczi László, Pap Gyula)
• Lineáris algebra és többváltozós függvények pdf
• Valószínűségszámítás pdf
• Előadáskövető jegyzet (szerzők: Losonczi László, Pap Gyula)
• Lineáris algebra és többváltozós függvények pdf
• Valószínűségszámítás pdf
• Előadáskövető fóliák (szerzők: Losonczi László, Pap Gyula) pdf
• Beadandó házi feladatok I. pdf
• Beadandó házi feladatok II. pdf
• A vizsgával kapcsolatos információk doc és minta feladatsor pdf

• Tételsor és vizsgainformációk doc

• Az előadás tematikája doc
• Tételsor és vizsgainformációk doc

Teaching

    Mathematics I:

• Course description doc
• Handout 1. pdf
• Handout 2. pdf

• Course description doc
• Handout 1. pdf
• Handout 2. pdf

Curriculum vitae

• born: Debrecen, 9 July 1968

• university studies: mathematician, mathematics teacher, English-Hungarian specialized translator, Lajos Kossuth University, 1987-1992

• PhD scholarship: 1993 - 1996

• assistant lecturer: 1996 - 1999

• assistant professor: 1999 - 2003

• associate professor: 2003 -

• PhD degree: 1998
  title of the thesis: Some new results on polynomials and diophantine equations

• habilitation: 2003
  title of the thesis: Recent results in diophantine number theory (in Hungarian)

•   MTA doctor degree: 2011
    title of the thesis: Arithmetic progressions in multiplicative sets (in Hungarian)
  

• postdoctor at Leiden University (Leiden, the Netherlands), host professor: Prof. Dr. Robert Tijdeman, 1999

• prizes:
  1992: Kató Rényi Prize of the János Bolyai Mathematical Society
  1994: László Patai Prize of the János Bolyai Mathematical Society
  1997: László Kalmár Prize of the University of Szeged
  1997: Géza Grünwald Prize of the János Bolyai Mathematical Society
  1999-2002: János Bolyai Research Fellowship of the Hungarian Academy of Sciences
  2001: Youth Academic Prize of the Hungarian Academy of Sciences
  2003: Chart of the Advisory Board of the János Bolyai Research Fellowship of the Hungarian Academy of Sciences
  2004-2007: János Bolyai Research Fellowship of the Hungarian Academy of Sciences
  2008: Turán Prize of the Secion of Mathematics of the Hungarian Academy of Sciences

• knowledge of languages: English (superlative), Russian (elementary)

• secretary of Mathematical TDK of Faculty of Sciences of University of Debrecen: 2001-2003

• secretary of the Mathematical Comittee of the Debrecen Committee of the Hungarian Academy of Sciences: 2002 - 2011

•   head of the Mathematical, Physical, Computer Science Comittee of the Debrecen Committee of the Hungarian Academy of Sciences: 2012 - 

• secretary of the Institute of Mathematics of University of Debrecen: 2003-2005

• secretary of the Mathematical Committee of the Secion of Mathematics of the Hungarian Academy of Sciences: 2005 - 2008
  

• reviewer of Zentralblatt für Mathematik and Mathematical Reviews

• secretary of the Doctoral Committee of the Secion of Mathematics of the Hungarian Academy of Sciences: 2010 -

Publications (The downlodable files are the pre-submission versions.)

SCI publications

[1] L. Hajdu, A quantitative version of Dirichlet's S-unit theorem in algebraic number fields, Publ. Math. Debrecen 42 (1993), 239-246. paper

[2] A. Bérczes and L. Hajdu, Computational experiences on the distances of polynomials to irreducible polynomials, Math. Comp. 66 (1997), 391-398. paper

[3] L. Hajdu, On a problem of Győry and Schinzel concerning polynomials, Acta Arith. 78 (1997), 287-295. paper

[4] L. Hajdu, On a diophantine equation concerning the number of integer points in special domains II, Publ. Math. Debrecen 51 (1997), 331-342. paper

[5] L. Hajdu, On a diophantine equation concerning the number of integer points in special domains, Acta Math. Hungar. 78 (1998), 59-70. paper

[6] A. Bérczes and L. Hajdu, On a problem of P. Turán concerning irreducible polynomials, in: Number Theory: Diophantine, Computational and Algebraic Aspects (K. Győry, A. Pethő and V. T. Sós eds.) 1998, pp. 95-101. paper

[7] L. Hajdu and T. Herendi, Explicit bounds for the solutions of elliptic equations with rational coefficients, J. Symbolic Computation 25 (1998), 361-366. paper

[8] A. Bérczes, B. Brindza and L. Hajdu, On power values of polynomials, Publ. Math. Debrecen 53 (1998), 375-381. paper

[9] L. Hajdu and Á. Pintér, Square product of three integers in short intervals, Math. Comp. 68 (1999), 1299-1301. paper
[10] B. Brindza, L. Hajdu and I. Z. Ruzsa, On the equation x(x+d)…(x+(k-1)d)=by², Glasgow Math. J. 42 (2000), 255-261. paper

[11] L. Hajdu and Á. Pintér, Combinatorial diophantine equations, Publ. Math. Debrecen 56 (2000), 391-403. paper
[12] Y. Bugeaud and L. Hajdu, Lower bounds for the difference |axⁿ-by^m|, Acta Math. Hungar. 87 (2000), 279-286. paper
[13] L. Hajdu and L. Szalay, On the Diophantine equations (2ⁿ-1)(6ⁿ-1)=x² and (aⁿ-1)(a^kn-1)=x², Period. Math. Hungar. 40 (2000), 141-145. paper
[14] P. Filakovszky and L. Hajdu, The resolution of the equation x(x+d)…(x+(k-1)d)=by² for fixed d, Acta Arith. 98 (2001), 151-154. paper

[15] L. Hajdu and R. Tijdeman, Algebraic aspects of discrete tomography, J. Reine Angew. Math. 534 (2001), 119-128. paper

[16] L. Hajdu and R. Tijdeman, An algorithm for discrete tomography, J. Linear Algebra 339 (2001), 147-169. paper

[17] A. Fazekas, A. Hajdu and L. Hajdu, Properties of generalized neighbourhood sequences in finite dimension, Proceedings of the 4th International Conference on Applied Informatics (E. Kovács, Z. Winkler, eds.), 2001, pp. 129-134. paper

[18] A. Fazekas, A. Hajdu and L. Hajdu, Lattice of generalized neighbourhood sequences in nD and ∞D, Publ. Math. Debrecen 60 (2002), 405-427. paper

[19] A. Fazekas, A. Hajdu and L. Hajdu, Analyzing the structure of neighbourhood sequences, Proceedings of the 5th International Conference on Applied Informatics, (E. Kovács, Z. Winkler, eds), 2002, pp. 41-47. paper

[20] L. Hajdu and R. Tijdeman, Algebraic aspects of emission tomography with absorption, Theoret. Comput. Sci. 290 (2003), 2169-2181. paper

[21] L. Hajdu and R. Tijdeman, Polynomials dividing infinitely many quadrinomials or quintinomials, Acta Arith. 107 (2003), 381-404. paper

[22] A. Hajdu and L. Hajdu, Velocity and distance of neighbourhood sequences, Acta Cybernet. 16 (2003), 133-145. paper
[23] K. Győry, L. Hajdu and N. Saradha, On the diophantine equation n(n+d)…(n+(k-1)d)=by^l, Canad. Math. Bull. 47 (2004), 373-388. Correction: Canad. Math. Bull. 48 (2005), 636. paper correction

[24] A. Hajdu and L. Hajdu, Approximating the Euclidean distance using non-periodic neighbourhood sequences, Discrete Math. 283 (2004), 101-111. paper

[25] K. Győry, L. Hajdu, Á. Pintér and A. Schinzel, Polynomials determined by a few of their coefficients, Indag. Math. 15 (2004), 209-221. paper

[26] L. Hajdu, Perfect powers in arithmetic progression. A note on the inhomogeneous case, Acta Arith. 113 (2004), 343-349. paper

[27] L. Hajdu, Irreducible polynomials in arithmetic progressions and a problem of Szegedy, Publ. Math. Debrecen 65 (2004), 363-370. paper
[28] A. Fazekas, A. Hajdu and L. Hajdu, Metrical neighborhood sequences Zⁿ, Pat. Rec. Let. 26 (2005), 2022-2032. paper

[29] L. Hajdu, Unique reconstruction of bounded sets in discrete tomography, Electronic Notes in Discrete Mathematics 20 (2005), 15-25. paper

[30] M. Bennett, N. Bruin, K. Győry and L. Hajdu, Powers from products of consecutive terms in arithmetic progression, Proc. London Math. Soc. 92 (2006), 273-306. paper

[31] G. Hajdu and L. Hajdu, On an identity of Ramanujan over finitely generated domains, Acta Math. Hungar. 112 (2006), 143-155. paper

[32] N. Bruin, K. Győry, L. Hajdu and Sz. Tengely, Arithmetic progressions consisting of unlike powers, Indag. Math. 17 (2006), 539-555. paper

[33] L. Hajdu and Zs. Turi Nagy, Power values of sums of polynomials, Publ. Math. Debrecen 69 (2006), 321-331. paper
[34] A. Hajdu, L. Hajdu and R. Tijdeman, General neighbourhood sequences in Zⁿ, Disc. Appl. Math. 155 (2007), 2507-2522. paper

[35] L. Hajdu and R. Tijdeman, Algebraic Discrete Tomography, in: Advances in Discrete Tomography and Its Applications (G. T. Herman and A. Kuba eds.), Birkhäuser, 2007, pp. 55-81. paper

[36] L. Hajdu, Arithmetic progressions in linear combinations of S-units, Period. Math. Hungar. 54 (2007), 175-181. paper
[37] A. Hajdu and L. Hajdu, On the lattice structure of subsets of octagonal neighbourhood sequences in Zⁿ, Lecture Notes in Computer Science, DGCI 2006 (A. Kuba, L. G. Nyúl, K. Palágyi eds.), LNCS 4245 (2007), 211-222. paper

[38] G. Hajdu and L. Hajdu, Hosszú's equation over the Gaussian- and Eisenstein-integers, Aequationes Math. 20 (2007), 1-10. paper

[39] L. Hajdu and R. Tijdeman, A criterion for polynomials to divide infinitely many k-nomials, Diophantine Approximations, (H. P. Schlickewei, K. Schmidt and R. F. Tichy, eds.), Developments in Mathematics 16, Springer-Verlag, 2008, pp. 211-220. paper

[40] L. Hajdu, Powerful arithmetic progressions, Indag. Math. 19 (2008), 547-561. paper

[41] L. Hajdu, Sz. Tengely and R. Tijdeman, Cubes in products of terms in arithmetic progression, Publ. Math Debrecen 74 (2009), 215-232. paper

[42] L. Hajdu and T. Kovács, Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations, Math. Comp. 78 (2009), 1201-1210. paper examples

[43] L. Hajdu and Sz. Tengely, Arithmetic progressions of squares, cubes and n-th powers, J. Functiones et Approximatio 41 (2009), 129-138. paper

[44] Zs. Ádám, L. Hajdu and F. Luca, Representing primes as linear combinations of pure powers, Acta Arith. 138 (2009), 101-107. paper

[45] K. Győry, L. Hajdu and Á. Pintér, Perfect powers from products of consecutive terms in arithmetic progression, Compositio Math. 145 (2009), 845-864. paper

[46] L. Hajdu, Optimal systems of fundamental S-units for LLL-reduction, Period. Math. Hungar. 59 (2009), 79-105. paper

[47] L. Hajdu, A. Schinzel and M. Skalba, Multiplicative properties of sets of positive integers, Archiv der Math. 93 (2009), 269-276. paper

[48] A. Bérczes, L. Hajdu and A. Pethő, Arithmetic progressions in the solution sets of norm form equations, Rocky Mountain J. Math. Rocky Mountain J. Math. 40 (2010), 383-395. paper

[49] L. Hajdu and N. Saradha, On a problem of Pillai and its generalizations, Acta Arith. 144 (2010), 323-347. paper tables

[50] L. Hajdu L. and F. Luca, On the length of arithmetic progressions in linear combinations of S-units, Archiv der Math. 94 (2010), 357-363. paper

[51] L. Hajdu and  N. Saradha, On a problem of Recaman and its generalization, J. Number Theory 131 (2011) 18-24. paper

[52] K. Győry, L. Hajdu and R. Tijdeman, Irreducibility criteria of Schur-type and Pólya-type, Monatsh. Math. 163 (2011), 369-380. paper

[53] K. J. Batenburg, W. Fortes, L. Hajdu and R. Tijdeman, Bounds on the difference between reconstructions in binary tomography, Discrete Geometry and Computer Imaginary, LNCS 6607 (2011), 369-380. paper

[54] Kovács L., Tomán H., Jónás Á., Hajdu L. és Hajdu A., Generalizing the majority voting scheme to conditional voting, Lecture Notes in Artificial Intelligence 6679 (2011), 189-196. paper

[55] L. Hajdu and T. Kovács, Almost fifth powers in arithmetic progressions, J. Number Theory 131 (2011), 18-24. paper

[56] L. Hajdu and N. Saradha, Disproof of a conjecture of Jacobsthal, Math. Comp. (accepted). paper

[57] L. Hajdu and R. Tijdeman, Representing integers as linear combinations of powers, Publ. Math. Debrecen 79 (2011), 461-468. paper

[58] A. Bérczes, A. Dujella, L. Hajdu and F. Luca, On the size of sets whose elements have perfect power n-shifted products, Publ. Math. Debrecen 79 (2011), 325-339. paper

[59] L. Hajdu, N. Saradha and R. Tijdeman, On a conjecture of Pomerance, Acta Arith. (accepted). paper

[60] L. Hajdu and R. Tijdeman, Representing integers as linear combinations of power products, Arch. Math. (accepted). paper

dissertations

other publications

[64] A. Fazekas, A. Hajdu and L. Hajdu, Structural analysis of finite dimensional sequences (in Hungarian), in: KéPAF'2000 (2000), 29-32.

[69] A. Fazekas, A. Hajdu and L. Hajdu, Lattices of metrical neighborhood sequences, in: Joint Hungarian-Austrian Conference on Image Processing and Pattern Recognition, (D. Chetverikov, L. Czúni and M. Vincze eds.), Oesterreichische Computer Gesellschaft, 2005, pp. 143-146.
[70] A. Hajdu, L. Hajdu and T. Tóth, Properties and applications of neighborhood sequences, Third Hungarian Conference on Computer Graphics and Geometry (2005), Budapest, Hungary, pp. 148-154. paper
[71] A. Fazekas, A. Hajdu and L. Hajdu, Properties of a natural ordering relation for octogonal neighborhood sequences, 5th International Symposium on Image and Signal Processing and Analysis (ISPA 2007), Istanbul, Turkey, 27-29 September 2007, pp. 168-173. paper

Talks

[1] On a problem of Turán concerning irreducible polynomials, 12th Czech and Slovak International Conference on Number Theory, Liptovsky Jan, 1995.

[2] On a problem of Győry and Schinzel concerning polynomials, Number Theory '96, Eger, 1996.

[3] On some combinatorial diophantine equations, Number Theory Conference, Zakopane, 1997.

[4] The resolution of some combinatorial diophantine equations, 13th Czech and Slovak International Conference on Number Theory, Ostravice, 1997.
[5] On the diophantine equation x(x+d)…(x+(k-1)d)=by², Number Theory '98, Graz, 1998.
[6] Lower bounds for the difference axⁿ-by^m, Number Theory Day, Debrecen, 1998.
[7] On the diophantine equation x(x+d)…(x+(k-1)d)=by², Number Theory Seminar, Austin, 1998.

[8] On superelliptic equations, Intercity Number Theory Seminar, Leiden, 1999.

[9] Lower bounds for the difference of almost perfect powers, Workshop on Diophantine Approximations, Oberwolfach, 2000.

[10] Polynomials dividing infinitely many quadrinomials or quintinomials II, Number Theory 2000, Debrecen, 2000.
[11] On the equation n(n+d)…(n+(k-1)d)=by^l, 15th Czech and Slovak International Conference on Number Theory, Ostravice, 2001.
[12] On the equation f(x)+g(x)=by^l, Workshop on Effective Methods for Diophantine Equations, Debrecen, 2001.

[13] Polynomials dividing infinitely many k-nomials, Number Theory Seminar, Leiden, 2002.
[14] On the diophantine equation n(n+d)…(n+(k-1)d)=by^l, Workshop on Explicit Algebraic Number Theory, Leiden, 2002.

[15] On the roots of sums of polynomials (in Hungarian), Conference on Number Theory to the Memory of Péter Kiss, Eger, 2002.

[16] Almost perfect powers in products of consecutive terms from an arithmetic progression, Workshop Diophantine Approximation, Leiden, 2003.

[17] Powers from products of consecutive terms in arithmetic progression, XXIIIrd Journées Arithmétiques, Graz, 2003.

[18] Almost perfect powers in arithmetic progression; Additive and multiplicative problems concerning polynomials; Neighborhood sequences; Discrete tomography (in Hungarian), Seminar of Institute of Mathematics, University of Debrecen, 2004.

[19] Metrical and approximation properties of neighborhood sequences (in Hungarian), KÉPAF’04 Conference, Miskolc-Tapolca, 2004.

[20] Inhomogeneous powers in arithmetic progression, Number Theory Seminar, Leoben, 2004.

[21] Perfect powers in arithmetic progressions (in Hungarian), Diophantine Day in Sopron, Sopron, 2004.

[22] On the problems of Turán and Szegedy concerning irreducible polynomials, Number Theory Seminar, Leiden, 2005.

[23] The problem of Turán and Szegedy concerning irreducible polynomials (in Hungarian), Cryptography and Diophantine Day in Nyíregyháza, Nyíregyháza, 2005.

[24] Unique reconstruction of bounded sets in discrete tomography, Discrete Tomography and its Applications, New York, 2005.

[25] Polynomials dividing infinitely many k-nomials, 17th Czech and Slovak International Conference on Number Theory, Malenovice, 2005.

[26] Perfect powers in arithmetic progressions (in Hungarian), Diophantine and Cryptography Days in Berekfürdő, Berekfürdő, 2006.
[27] On the Lattice Structure of Subsets of Octagonal Neighborhood Sequences in Zⁿ (poster), 13th International Conference on Discrete Geometry for Computer Imagery, Szeged, 25-27 October 2006.

[28] Perfect powers in arithmetic progressions, Solvability of Diophantine Equations, Leiden, 14-16 May 2007.

[29] Perfect powers in arithmetic progressions, XXVth Journées Arithmétiques, Edinburgh, 2-7 July 2007.

[30] Arithmetic progressions in linear combinations of S-units, 18th Czech and Slovak International Conference on Number Theory, Smolenice, 27-31 August 2007.
[31] Perfect powers in arithmetic progression, Seminar of TATA Institute of Fundamental Research, Mumbai, 21 February 2008.

[32] Almost perfect powers in arithmetic progression, Czech, Slovak and Polish Number Theory Conference, Ostravice, 10-14 June, 2008.

[33] Neighborhood sequences and their applications, Robert Tijdeman 65, Symposium Number Theory & Discrete Mathematics, Leiden, 27-28 August, 2008.

[34] Full powers in arithmetic progression (in Hungarian), Soproni Diofantikus és Kriptográfiai Napok, 10-12 October, 2008

[35] Perfect powers in arithmetic progression, PALI65 Conference, Debrecen, 21-24 October, 2008.

[36] Perfect powers in arithmetic progression, Winter School on the explicit solution of Diophantine equations, Debrecen, 26-30 January, 2009.

[37] Perfect powers in arithmetic progression (in Hungarian), Number Theory Seminar of the Rényi Institute, 24 February, 2009.

[38] Perfect powers in arithmetic progression, Nihon University of Tokyo, Number Theory Seminar, 22 May 2009.

[39] Perfect powers in arithmetic progression, University of Niigata, Number Theory Seminar, 26 May 2009.

[40] Perfect powers in arithmetic progression, Sangyo University of Kyoto, Number Theory Seminar, 30 May 2009

[41] Perfect powers in arithmetic progression, XXVIth Journées Arithmétiques, St. Etienne, 10 July 2009.

[42] Arithmetical properties of sets of linear combinations of S-units, First conference on Algebra and Number Theory, Ixtapa, Mexikó, 30 July 2009.

[43] Algebraic tomography and its applications, Meeting on Discrete and Geometric Tomography, and Applications to Computer Algorithms, Milánó, Olaszország, April 22-23 2010.

[44] Inhomogeneous powers in arithmetic progressions, Bukowina Tatrzanska, Lengyelország, Algebra, Logic and Number Theory Conference, 21-24 July 2010.

[45] Mixed powers in arithmetic progression, Acadia University, Wolfville, Kanada, CNTA XI Conference, 11-16 July 2010.

[46] The importance of a special constant in bounding the solutions of S-unit equations, Approximation diophantienne et transcendance, Marseille-Luminy, September 6-10 2010.

[47] Prímlefedések és legnagyobb közös osztók: Pillai egy problémája illetve a Jacobsthal-függvény és alkalmazásai, Rényi Alfréd Matematikai Kutatóintézet, Számelmélet szeminárium, 2010. szeptember 28.

[48] Perfect powers in arithmetic progression, Number Theory and its Applications, An International Conference Dedicated to Kálmán Győry, Attila Pethő, János Pintz, András Sárközy, Debrecen, October 4-8 2010.

[49] Mixed powers in arithmetic progression, Number Theory Seminar of Zagreb University, 2011. január 26.

[50] On a conjecture of Pomerance and the Jacobsthal function, 27th Journées Arithmétiques, Vilnius, Litvánia, 2011. június 27- július 1.

[51] Representation problems with linear combinations of units, Paul Turán Memorial Conference, Budapest, 2011. augusztus 22-26.

[52] A problem of Pillai and its generalizations, 20th Czech and Slovak International Conference on Number Theory, Stará Lesná, Szlovákia, 2011. szeptember 5-9.

[53] Representation problems with linear combinations of units, Number Theory Seminar, Graz, Austria, 2011. november 18.

Last updated: 2012. 03. 10.