Research
- A. Pethő and Sz. Tengely: Common values of linear recurrences related to Shank's simplest cubics, Submitted for publication (2024).
- L. Hajdu, Sz. Tengely and M. Ulas: Products of Catalan numbers which are squares, Submitted for publication (2024).
- L. Hajdu, O. Herendi, Sz. Tengely and N. Varga: Square Values of Littlewood Polynomials, Submitted for publication (2024).
- A. Bazsó, I. Mező, Á. Pintér and Sz. Tengely: Singmaster-type results for Stirling numbers and some related Diophantine equations, Submitted for publication (2024).
- Sz. Tengely and M. Ulas: Diophantine problems related to cyclic cubic and quartic fields, Journal of Number Theory 240 656–684 (2022).
- H. Hashim, L. Szalay and Sz. Tengely: Markoff-Rosenberger triples and generalized Lucas sequences, Period. Math. Hung. 85, No. 1, 188-202 (2022).
- H. Hashim and Sz. Tengely: Lucas sequences and repdigits, Math. Bohem. 147, No. 3, 301-318 (2022).
- Sz. Tengely and M. Ulas: Equal values of certain partition functions via Diophantine equations, Research in Number Theory 7, Article number: 67 (2021).
- Sz. Tengely, M. Ulas and J. Zygadlo: On a Diophantine equation of Erdős and Graham,J. Number Theory 217, 445-459 (2020).
- Sz. Tengely and M. Ulas: On the Diophantine equation \(F_n=P(x)\),Int. J. of Number Theory 16, 2095-2111 (2020).
- L. Hajdu and Sz. Tengely: Powers in arithmetic progressions, accepted, The Ramanujan Journal.
- H. Hashim and Sz. Tengely: Solutions of a Generalized Markoff Equation with Fibonacci Components, Math. Slovaca 70, 1069–1078 (2020).
- Sz. Tengely: Markoff-Rosenberger triples with Fibonacci components, Glasnik Math 55, 29-36 (2020).
- H. R. Gallegos-Ruiz, N. Katsipis, Sz. Tengely and M. Ulas: On the Diophantine equation \(\binom{n}{k}=\binom{m}{l}+d\), J. Number Theory 208, 418-440 (2020).
- H. Hashim and Sz. Tengely: Diophantine equations related to reciprocals of linear recurrence sequences, Notes on Number Theory and Discrete Mathematics, Volume 25, 2019, Number 2, Pages 49-56
- H. Hashim and Sz. Tengely: Representations of reciprocals of Lucas sequences, Miskolc Math. Notes 19, No. 2, 865-872 (2018).
- Sz. Tengely and M. Ulas: Power values of sums of certain products of consecutive integers and related results, J. Number Theory 197, 341-360 (2019).
- Sz. Tengely and M. Ulas: On a problem of Pethő, J. Symb. Comput. 89, 216-226 (2018).
- Sz. Tengely: Trinomials \(ax^8+bx+c\) with Galois groups of order 1344, Glasnik Matematicki, Glas. Mat., III. Ser. 53, No. 2, 265-273 (2018).
- Sz. Tengely and M. Ulas: On certain Diophantine equations of the form \(z^2=f(x)^2\pm g(y)^2\), J. Number Theory 174 (2017), 239–257.
- Sz. Tengely: Composite Rational Functions and Arithmetic Progressions, Publ. Math. Debrecen 92 (2018), no. 1-2, 115–132.
- Sz. Tengely and M. Ulas: On products of disjoint blocks of arithmetic progressions and related equations, Journal of Number Theory Volume 165., 67-83.
- L. Hajdu, S. Laishram and Sz. Tengely: Power values of sums of products of consecutive integers, Acta Arith. 172 (2016), no. 4, 333–349.
- A. Bérczes, A. Dujella, L. Hajdu and Sz. Tengely: Finiteness results for F-Diophantine sets, Monatsh. Math. 180 (2016), no. 3, 469–484.
- Sz. Tengely: Integral points and arithmetic progressions on Huff curves, submitted.
- Sz. Tengely: On a problem of Erdős and Graham, Period. Math. Hungar. 72 (2016), no. 1, 23–28.
- Sz. Tengely: On the Lucas sequence equation \(\frac{1}{U_n}=\sum_{k=1}^{\infty}\frac{U_{k-1}}{x^k}\), Period. Math. Hungar. 71 (2015), no. 2, 236–242.
- L. Hajdu, Á. Pintér, Sz. Tengely and N. Varga: Equal Values of Figurate Numbers, J. Number Theory 137 (2014), 130–141.
- M. A. Alekseyev and Sz. Tengely:
On integral points on biquadratic curves and near multiples of squares in Lucas sequences, J. Integer Seq. 17 (2014), no. 6, Article 14.6.6, 15 pp.
SAGE code: biquadratic.sage - Sz. Tengely and N. Varga: Rational function variant of a problem of Erdős and Graham, Glas. Mat. Ser. III 50(70) (2015), no. 1, 65–76.
- Sz. Tengely and N. Varga: On a generalization of a problem of Erdős and Graham, Publ. Math. Debrecen 84 (2014), no. 3-4, 475–482.
- A. Pethő and Sz. Tengely:
On Composite Rational Functions, Number theory, analysis, and combinatorics, 241–259,
De Gruyter Proc. Math., De Gruyter, Berlin, 2014.
MAGMA code to compute systems: CFunc.m
Systems in case of n=5: CFunc_n=5.txt.tar.gz - Balancing numbers which are products of consecutive integers, Publ. Math. Debrecen 83 (2013), no. 1-2, 197–205.
- Á. Pintér and Sz. Tengely: The Korteweg-De Vries Equation and a Diophantine Problem Related to Bernoulli polynomials, Adv. Difference Equ. 2013, 2013:245, 9 pp.
- C. Fuchs, A. Pethő and Sz. Tengely: On decomposable rational functions with given number of singularities, Proceedings of the RIMS Symposium Algebraic Systems and Theoretical Computer Science, RIMS Kôkyûroku, 1809, 54-64, (2012)
- On the Diophantine equation \(L_n=\binom{x}{5}\), Publ. Math. Debrecen 79 (2011) 749-758.
- Algebrai görbék a diofantikus számelméletben, Habilitation Thesis, University of Debrecen (2010)
TezisekTSz.pdf - Finding g-gonal numbers in recurrence sequences, Fibonacci Quarterly 46/47:(3) (2009) 235-240.
- F. Luca, Sz. Tengely and A. Togbé: On the Diophantine Equation \(x^2 + C = 4y^n\), Ann. Sci. Math. Québec 33:(2) (2009) 171-184.
- L. Hajdu, Sz. Tengely and R. Tijdeman: Cubes in products of terms in arithmetic progression, Publ. Math. Debrecen 74 (2009) 215-232.
- L. Hajdu and Sz. Tengely: Arithmetic progressions of squares, cubes and n-th powers, Functiones et Approximatio, Commentarii Mathematici 41:(2) (2009) 129-138.
- F. S. Abu Muriefah, F. Luca, S. Siksek and Sz. Tengely: On the Diophantine Equation \(x^2+C=2y^n\), International Journal of Number Theory 5:(6) (2009) 1117-1128.
- Y. Bugeaud, M. Mignotte, S. Siksek, M. Stoll and Sz. Tengely: Integral Points on Hyperelliptic Curves, Algebra and Num. Th. 2 (2008) 859-885.
- Note on a paper "An Extension of a Theorem of Euler" by Hirata-Kohno et al., Acta Arith. 134 (2008) 329-335.
- S. Laishram, T. N. Shorey and Sz. Tengely: Squares in products in arithmetic progression with at most one term omitted and common difference a prime power, Acta Arith. 135 (2008) 143-158.
- On the Diophantine equation \(x^2+q^{2m}=2y^p\), Acta Arith. 127 (2007) 71-86.
- Triangles with two integral sides, Annales Mathematicae et Informaticae 34 (2007) 89-95.
- F. Beukers and Sz. Tengely: An implementation of Runge's method for Diophantine equations
- N. Bruin, K. Győry, L. Hajdu and Sz. Tengely: Arithmetic progressions consisting of unlike powers, Indag. Math. (N.S.) 17 (2006), 539-555.
- Effective Methods for Diophantine Equations, (Ph.D. thesis, Leiden University, The Netherlands, 2005, under the supervision of Rob Tijdeman)
Stellingen.pdf
Cover.pdf - On the Diophantine equation \(x^2+a^2=2y^p\), Indag. Math. (N.S.) 15 (2004), 291-304.
- On the Diophantine equation \(F(x)=G(y)\), Acta Arith. 110 (2003), 185-200.
- I. Pink and Sz. Tengely: Full powers in arithmetic progressions, Publ. Math. Debrecen 57 (2000), 535-545.
- A \(D_1(a_0x^2+a_1x+a_2)^2+D_2(b_0y^2+b_1y+b_2)=k\) diofantikus egyenlet effektív és numerikus vizsgálata, MSc Thesis, Lajos Kossuth University, Debrecen, 1999.
K. Dsupin and Sz. Tengely:
Discrete logarithm problem in some families of sandpile groups, 2020.
H. R. Hashim, A. Molnár and Sz. Tengely:
Cryptanalysis of ITRU, 2020.
Sz. Tengely:
Lecture Notes on Cryptography, 2020.
C. Henkel, P. Frisco and Sz. Tengely:
An algorithm for SAT without an extraction phase, DNA Computing, Eleventh International Meeting on DNA Based Computers, LNCS. Vol. 3892, ISBN: 3-540-34161-7, 67-80.
I have written a program in Matlab to illustrate the algorithm of
Hajdu and Tijdeman. Here you can download the program and the article
of Hajdu and Tijdeman. You also find a README file for the program.