**Nikos**
**(Nikolaos)
G.
Tzanakis ****- Research Publications**

(with P. Voutier), *Near-squares
in binary recurrence sequences*, Int. J. Number Theory (to
appear)

(with P. Das,
P. K. Dey, A. Koutsianas), *Perfect powers
in sum of three fifth powers*^{}.
J. Number Theory 236
(2022) 443-462.

(with G.
Soydan), *Complete solution of the Diophantine
equation x*^{2 }*+ 5*^{a}
*11*^{b}
*= y*
^{n}.
Bull. Hellenic Math. Soc.
60 (2016), 125-151.

(with A.
Laradji, M. Mignotte), *A
trigonometric sum related to quadratic residues,*
Elem. Math. **67**
(2012),
no
2, 51-60.

(with R.
Schoof), *Integral
points of a modular curve of level 11*,
__Acta
Arith.__ **152** (2012), 39-49.

(with A. Laradji, M. Mignotte), *On px*^{2}
*+ q*^{2n}*= y*^{p}
*and
related Diophantine equations*, __J.
Number Theory__ **131 **(2011), 1575-1596.

*Important remark* *(August 2021):* The link to this paper
refers to the updated version (October 2020) of the paper, whose main
feature is the correction of Theorem 3.2.

(with A. Bremner), *On the equation Y*^{2} *= X*^{6}
*+ k*, (dedicated
to professor Paulo Ribenboim on the occasion of his 80th birthday) __Annales des Sciences Math____è____matiques du Qu____é____bec__, **35**, no 2 (2011), 153-174.

(with
I.N. Cangül, M. Demirci, G. Soydan) , *On the
Diophantine equation x*^{2 }*+ 5*^{a}
*11*^{b}
*= y*
^{n}. __Funct. Approx.
Comment. Math.__ **43.2** (2010), 209-225.

(with A.
Bremner) *Lucas
sequences whose n-*th *term is a
square or an almost square*,
__Acta____ ____Arithm.__ **126.3** (2007),
261-280.

(with A.
Bremner) *On squares in Lucas sequences*
, __J. Number Theory__
**124**
(2007),
511-520.

·
(with A.
Bremner) *Lucas
sequences whose 12th and 9th term is a square* , __J. Number Theory__
**107 **(2004), 215-227.

*Extended
version
of the paper. *

·
(with R.J.
Stroeker) *Computing all
integer solutions of a genus 1 equation,* __Math.Comp__. **72 **(2003), 1917-1933.

The
impressive rational
functions X*(u,v)* και Y*(u,v) *of section 3.2

·
*Effective solution of two simultaneous
Pell equations by the Elliptic Logarithm Method*, __Acta Arithm__. **103**
(2002),
119-135.

·
(with R.J.
Stroeker) *Computing all
integer solutions of a general elliptic equation*
Proceedings of
the 4th International Symposium in Algorithmic Number Theory, W. Bosma
(Ed), *Lecture
Notes in Computer Science ***1838***, *p.p.551-561, Springer 2000.

·
(with A.
Bremner and J.H. Silverman) *Integral
points in arithmetic progressions on * *y*^{2} *= x(x*^{2}*-n*^{2}*)*, __J.Number Theory__ **80 **(2000), 187-208.

·
(with
R.J.Stroeker) *On*
*the
elliptic logarithm method for elliptic diophantine equations:*
*Reflections
and an improvement*, __Experimental Math__. **8**
(1999),
135-149.

·
(with A.
Bremner and R .J. Stroeker) *On*
*sums of
consecutive squares*, __J.Number Theory__ **62** (1997), 39-70.

·
*Solving* *elliptic diophantine equations by
estimating linear forms in elliptic logarithms. The quartic
case*, __Acta Arithm__. **75** (1996), 165-190. (The file here is of the
extended --computational details included-- and revised (May 2012)
version.)

·
(with
R.J.Stroeker) *Solving
elliptic diophantine equations by estimating linear forms in
elliptic logarithms*, __Acta Arith.__ **67** (1994),177-196. (The file here contains
correction in the Appendix.)

·
*Explicit solution of a class of quartic Thue
equations* __Acta
Arith.__ **64**
(1993), 271-283.

·
(with
M.Mignotte) *Arithmetical
study
of a certain ternary recurrence sequence and related equations,*
__Math.Comp__. **61**
(1993),
901-913.

·
(with B.M.M.de
Weger *How to
explicitly solve a Thue-Mahler equation*, __Compositio.____
____Math__. **84**, (1992), 223-288.

*Corrections to
"How to explicitly solve a Thue-Mahler equation"*, Compositio Math.**89**
(1993),
241-242.

·
(with B.M.M.de Weger) *On
the
practical solution of the Thue-Mahler equation*,
__Proc. Debrecen Conference on Computational
Number Theory__, Walter de Gruyter &
Co., Berlin-New York 1991, p.p.289-294.

·
(with B.M.M.de
Weger) *Solving a
specific Thue-Mahler equation*, __Math.Comp__. **57** (1991), 799-815.

·
(with M.
Mignotte) *On a family of
cubics*, __J.Number Theory__ **39** (1991),41-49.

·
(with M. Mignotte) *Arithmetical study of recurrence sequences*, __Acta Arith.__ **57** (1991),
357-364.

·
(with J.Buchmann, K.Gÿory and M.Mignotte) *Lower bounds for P( x*^{3}
*+ k ), an elementary approach*,
__Publ. Math. Debrecen__ **38**(1991), 145-163.

·
(with
R.P.Steiner) *Simplifying
the solution of Ljunggren's equation x*^{2}
*+ 1 = 2y*^{4}, __J. Number Theory__ **37**
(1991),
123-132.

·
(with B.M.M. de
Weger) *On the
practical solution of the Thue equation*, __J.Number Theory__**31**
(1989), 99-132.

·
(with R.
J.Stroeker) *On
the
application of Skolem's p-adic method to the solution of Thue
equations,* __J.Number Theory__ **29** (1988) , 166 - 195.

·
*On* *the practical
solution of the Thue equation-An outline*,
__Colloq. Math. Soc. Janos Bolyai__ **51**, Number Th., Budapest 1987, p.p.1003-1012.

·
(with
J.Wolfskill) *The
diophantine equation y*^{2} *= 4q*^{a/2} *+ 4q + 1 with an application to Coding
Theory*, __J. Number Theory__ **26** (1987), 96-116.

·
(with
J.Wolfskill)__ ____On the
diophantine equation y__^{2}__
____= 4q__^{n}__
____+ 4q +
1____ __, __J. Number Theory__ **23**, 219-237.

· * On
the
diophantine equation x*^{2}* - Dy*^{4}* = k *
__Acta Arith.__ **46** (1986), 257-269.

·
*A* *remark on a
theorem of W.E.H.Berwick*, __Math. Comp__. **46** (1986), 623-625.

·
*On the diophantine equation 2x*^{3} *+ 1 = py*^{2}^{ },
__Manuscripta Math__. **54** (1985), 145-164.

·
*The complete solution in integers of x*^{3} *+ 3y*^{3}^{ }*=
2*^{n}^{
},
__J. Number Theory__ **19** (1984), 203-208.

·
*The* *diophantine
equation x*^{3}
*- 3xy*^{2}
*- y*^{3}
*= 1 and related equations*,
__J .Number Theory__
**18** (1984),
192-205.

·
(with A.Bremner) *Integer points on y*^{2}
*= x*^{3}
*- 7x + 10*, __Math.Comp__. **41** (1983), 731-741.

·
*On the diophantine equation y*^{2}
*- D = 2*^{k}
,
__J.Number Theory__ **17 **(1983), 144-164.

·
*The diophantine equation x*^{3}
*+ 3y*^{3}^{
}*= 2*^{n}
,
__J.Number Theory__ **15** (1982), 376-387.

Last update: 3 November 2023