TY  - JOUR
AU  - Behera, A
AU  - Liptai, Kálmán
AU  - Panda, G K
AU  - Szalay, László
TI  - Balancing with Fibonacci powers
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 49
PY  - 2011
IS  - 1
SP  - 28
EP  - 33
PG  - 6
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/1781112
ID  - 1781112
AB  - The Diophantine equation F1k + F2k + ⋯ + Fn-1k = Fn+1l + Fn+2l + ⋯ + Fn+rl in positive integers n,r,k,l with n ≥ 2 is studied where F n is the nth term of the Fibonacci sequence.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bérczes, Attila
AU  - Liptai, Kálmán
AU  - Pink, István
TI  - On generalized balancing sequences
JF  - FIBONACCI QUARTERLY
J2  - FIBONACCI QUART
VL  - 48
PY  - 2010
IS  - 2
SP  - 121
EP  - 128
PG  - 8
SN  - 0015-0517
UR  - https://m2.mtmt.hu/api/publication/1427122
ID  - 1427122
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
AU  - Tengely, Szabolcs
TI  - Arithmetic progressions of squares, cubes and n-th powers
JF  - FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI
J2  - FUNCT APPROX COMMENT MATH
VL  - 41
PY  - 2009
IS  - 2
SP  - 129
EP  - 138
PG  - 10
SN  - 0208-6573
DO  - 10.7169/facm/1261157805
UR  - https://m2.mtmt.hu/api/publication/1105972
ID  - 1105972
AB  - In this paper we continue the investigations about unlike powers in arithmetic progression. We provide sharp upper bounds for the length of primitive non-constant arithmetic progressions consisting of squares/cubes and n-th powers.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
AU  - Tijdeman, R
AU  - Tengely, Szabolcs
TI  - Cubes in products of terms in arithmetic progression
JF  - PUBLICATIONES MATHEMATICAE DEBRECEN
J2  - PUBL MATH DEBRECEN
VL  - 74
PY  - 2009
IS  - 1-2
SP  - 215
EP  - 232
PG  - 18
SN  - 0033-3883
UR  - https://m2.mtmt.hu/api/publication/1105971
ID  - 1105971
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Liptai, Kálmán
AU  - Luca, F
AU  - Pintér, Ákos
AU  - Szalay, László
TI  - Generalized balancing numbers
JF  - INDAGATIONES MATHEMATICAE-NEW SERIES
J2  - INDAGAT MATH NEW SER
VL  - 20
PY  - 2009
IS  - 1
SP  - 87
EP  - 100
PG  - 14
SN  - 0019-3577
DO  - 10.1016/S0019-3577(09)80005-0
UR  - https://m2.mtmt.hu/api/publication/1111765
ID  - 1111765
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
TI  - Powerful arithmetic progressions
JF  - INDAGATIONES MATHEMATICAE-NEW SERIES
J2  - INDAGAT MATH NEW SER
VL  - 19
PY  - 2008
IS  - 4
SP  - 547
EP  - 561
PG  - 15
SN  - 0019-3577
DO  - 10.1016/S0019-3577(09)00012-3
UR  - https://m2.mtmt.hu/api/publication/1242214
ID  - 1242214
N1  - Cited By :2            
            Export Date: 16 June 2023            
            CODEN: IMTHB            
            Correspondence Address: Hajdu, L.; University of Debrecen, P.O. Box 12, Debrecen, H-4010, Hungary; email: hajdul@math.klte.hu            
            Funding details: Magyar Tudományos Akadémia, MTA            
            Funding details: Hungarian Scientific Research Fund, OTKA, T48791            
            Funding text 1: Perfect powers, Arithmetic progression in part by the Hungarian Academy of Sciences and by the OTKA grants T48791
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Luca, F
AU  - Szalay, László
TI  - Fibonacci diophantine triples
JF  - GLASNIK MATEMATICKI
J2  - GLASNIK MAT
VL  - 43
PY  - 2008
IS  - 2
SP  - 253
EP  - 264
PG  - 12
SN  - 0017-095X
DO  - 10.3336/gm.43.2.03
UR  - https://m2.mtmt.hu/api/publication/1781118
ID  - 1781118
N1  - Megjegyzés-22289413
WC: Mathematics, Applied; Mathematics
Megjegyzés-22301580
WC: Mathematics, Applied; Mathematics
AB  - In this paper, we show that there are no three distinct positive integers a, b, c such that ab +1, ac + 1, bc +1 are all three Fibonacci numbers.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Pintér, Ákos
AU  - Rakaczki, Csaba
TI  - On the zeros of shifted Bernoulli polynomials
JF  - APPLIED MATHEMATICS AND COMPUTATION
J2  - APPL MATH COMPUT
VL  - 187
PY  - 2007
SP  - 379
EP  - 383
PG  - 5
SN  - 0096-3003
DO  - 10.1016/j.amc.2006.08.136
UR  - https://m2.mtmt.hu/api/publication/1111293
ID  - 1111293
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Szalay, László
TI  - On the resolution of simultaneous Pell equations
JF  - ANNALES MATHEMATICAE ET INFORMATICAE
J2  - ANN MATH INFORM
VL  - 34
PY  - 2007
SP  - 77
EP  - 87
PG  - 11
SN  - 1787-5021
UR  - https://m2.mtmt.hu/api/publication/1805873
ID  - 1805873
N1  - Jogelőd folyóirat (címváltozás): Acta Academiae Pedagogica 
Agriensis, Sectio Mathematicae
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bennett, MA
AU  - Győry, Kálmán
AU  - Mignotte, M
AU  - Pintér, Ákos
TI  - Binomial Thue equations and polynomial powers
JF  - COMPOSITIO MATHEMATICA
J2  - COMPOS MATH
VL  - 142
PY  - 2006
IS  - 5
SP  - 1103
EP  - 1121
PG  - 19
SN  - 0010-437X
DO  - 10.1112/S0010437X06002181
UR  - https://m2.mtmt.hu/api/publication/1111296
ID  - 1111296
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Bruin, N
AU  - Győry, Kálmán
AU  - Hajdu, Lajos
AU  - Tengely, Szabolcs
TI  - Arithmetic progressions consisting of unlike powers
JF  - INDAGATIONES MATHEMATICAE-NEW SERIES
J2  - INDAGAT MATH NEW SER
VL  - 17
PY  - 2006
IS  - 4
SP  - 539
EP  - 555
PG  - 17
SN  - 0019-3577
DO  - 10.1016/S0019-3577(07)00002-X
UR  - https://m2.mtmt.hu/api/publication/1073987
ID  - 1073987
AB  - In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given k >= 4 and L >= 3 there are only finitely many arithmetic progressions of the form (x(0)(l0), x(1)(l1),..., x(k-1)(lk-1)) with x(i) epsilon Z, gcd(x(0), x(1))= 1 and 2 <= l(i) <= L for i = 0, 1,...,k - 1. Furthermore, we show that, for L = 3, the progression (1, 1,..., 1) is the only such progression up to sign. Our proofs involve some well-known theorems of Faltings [9], Darmon and Granville [6] as well as Chabauty's method applied to superelliptic curves.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
AU  - Pintér, Ákos
TI  - Combinatorial diophantine equations
JF  - PUBLICATIONES MATHEMATICAE DEBRECEN
J2  - PUBL MATH DEBRECEN
VL  - 56
PY  - 2000
IS  - 3-4
SP  - 391
EP  - 403
PG  - 13
SN  - 0033-3883
UR  - https://m2.mtmt.hu/api/publication/1111355
ID  - 1111355
AB  - In this paper some diophantine equations concerning binomial
coefficients, power sums and product of consecutive integers are
resolved. The equations are reduced to elliptic equations and then the
program package SIMATH is used to determine the solutions.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
AU  - Pintér, Ákos
TI  - Square product of three integers in short intervals
JF  - MATHEMATICS OF COMPUTATION
J2  - MATH COMPUT
VL  - 68
PY  - 1999
IS  - 227
SP  - 1299
EP  - 1301
PG  - 3
SN  - 0025-5718
DO  - 10.1090/S0025-5718-99-01095-9
UR  - https://m2.mtmt.hu/api/publication/1111354
ID  - 1111354
AB  - In this paper we list all the integer triplets taken from an interval
of length less than or equal to 12, whose products are perfect squares.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
TI  - On a diophantine equation concerning the number of integer points in special domains
JF  - ACTA MATHEMATICA HUNGARICA
J2  - ACTA MATH HUNG
VL  - 78
PY  - 1998
IS  - 1-2
SP  - 59
EP  - 70
PG  - 12
SN  - 0236-5294
DO  - 10.1023/A:1006518403429
UR  - https://m2.mtmt.hu/api/publication/1242118
ID  - 1242118
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Pintér, Ákos
AU  - Benjamin, M M De Weger
TI  - 210 = 14 × 15 = 5 × 6 × 7 = (21 2) = (10 4)
JF  - PUBLICATIONES MATHEMATICAE DEBRECEN
J2  - PUBL MATH DEBRECEN
VL  - 51
PY  - 1997
IS  - 1-2
SP  - 175
EP  - 189
PG  - 15
SN  - 0033-3883
UR  - https://m2.mtmt.hu/api/publication/3211051
ID  - 3211051
N1  - Címben (21 2) és (10 4) binomiális együtthatók
WoS:hiba:A1997XV29400016 2019-03-09 22:14 első szerző nem egyezik
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Hajdu, Lajos
TI  - On a diophantine equation concerning the number of integer points in special domains II
JF  - PUBLICATIONES MATHEMATICAE DEBRECEN
J2  - PUBL MATH DEBRECEN
VL  - 51
PY  - 1997
IS  - 3-4
SP  - 331
EP  - 342
PG  - 12
SN  - 0033-3883
UR  - https://m2.mtmt.hu/api/publication/1242115
ID  - 1242115
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Brindza, B
AU  - Pintér, Ákos
TI  - On equal values of power sums
JF  - ACTA ARITHMETICA
J2  - ACTA ARITH
VL  - 77
PY  - 1996
IS  - 1
SP  - 97
EP  - 101
PG  - 5
SN  - 0065-1036
DO  - 10.4064/aa-77-1-97-101
UR  - https://m2.mtmt.hu/api/publication/1111347
ID  - 1111347
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Pintér, Ákos
TI  - A note on the Diophantine equation binom{x}{4}=binom{y}{2}
JF  - PUBLICATIONES MATHEMATICAE DEBRECEN
J2  - PUBL MATH DEBRECEN
VL  - 47
PY  - 1995
IS  - 3-4
SP  - 411
EP  - 415
PG  - 5
SN  - 0033-3883
UR  - https://m2.mtmt.hu/api/publication/1111861
ID  - 1111861
LA  - English
DB  - MTMT
ER  -