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

(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
Arithm.__
**152**
(2012),
39-49.

(with
A. Laradji, M. Mignotte), *On
px*^{2}
*+ q*^{2n}*=
y*^{p}
*and
related Diophantine equations*,
__J.
Number Th.__ **131
**(2011),
1575-1596. (No 4 to Top
25 articles published in 2011 J. Number Th.)

(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 Th.__ **124**
(2007),
511-520.

·
(with A.
Bremner) *Lucas
sequences whose 12th and 9th term is a square* ,
__J.
Number Th.__ **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
Th__.
**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
Th__.
**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
Arithm__.
**67**
(1994),177-196.
(The file here contains correction in the Appendix.)

·
*Explicit
solution of a class of quartic Thue equations*
__Acta Arithm__.
**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
Th__.
**39**
(1991),41-49.

·
(with M. Mignotte) *Arithmetical
study of recurrence sequences*, __Acta
Arithm__. **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 Th__.
**37**
(1991),
123-132.

·
(with B.M.M.
de Weger) *On
the practical solution of the Thue equation*,
__J.Number
Th__.**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
Th__.
**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 Th__.
**26**
(1987),
96-116.

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

· *
On
the diophantine equation x*^{2}*
- Dy*^{4}*
= k * __Acta Arithm__.
**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}^{
},
__Manuscr. Math__.
**54** (1985),
145-164.

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

·
*The* *diophantine
equation x*^{3} *-
3xy*^{2} *-
y*^{3} *=
1 and related equations*, __J
.Number Th__. **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 Th__. **17
**(1983), 144-164.

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

Last update: 9 March 2017