Nikos (Nikolaos) G. Tzanakis - Research Publications
(with R. Schoof), Integral points of a modular curve of level 11, Acta Arithm. 152 (2012), 39-49.
(with A. Laradji, M. Mignotte), On px2 + q2n= yp and related Diophantine equations, J. Number Th. 131 (2011), 1575-1596.
(with A. Laradji, M. Mignotte), A trigonometric sum related to quadratic residues, (submitted)
(with A. Bremner), On
the equation Y2
= X6
+ k,
(dedicated to professor Paulo
Ribenboim on the occasion of his 80th birthday) Annales
des Sciences Mathèmatiques
du Québec,
35,
no 2 (2011), 153-174.
(with
I.N. Cangül, M. Demirci, G. Soydan) , On
the Diophantine equation x2
+
5a
11b
= 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 y2 = x(x2-n2), 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.
· (with R.J.Stroeker) Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta Arithm. 67 (1994),177-196.
· 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.Gy'o'ry and M.Mignotte) Lower bounds for P( x3 + k ), an elementary approach, Publ. Math. Debrecen 38(1991), 145-163.
· (with R.P.Steiner) Simplifying the solution of Ljunggren's equation x2 + 1 = 2y4, 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 y2 = 4qa/2 + 4q + 1 with an application to Coding Theory, J. Number Th. 26 (1987), 96-116.
· (with J.Wolfskill) On the diophantine equation y2 = 4qn + 4q + 1 , J. Number Th. 23, 219-237.
· On the diophantine equation x2 - Dy4 = 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 2x3 + 1 = py2 , Manuscr. Math. 54 (1985), 145-164.
· The complete solution in integers of x3 + 3y3 = 2n , J. Number Th. 19 (1984), 203-208.
· The diophantine equation x3 - 3xy2 - y3 = 1 and related equations, J .Number Th. 18 (1984), 192-205.
· (with A.Bremner) Integer points on y2 = x3 - 7x + 10, Math.Comp. 41 (1983), 731-741.
· On the diophantine equation y2 - D = 2k , J.Number Th. 17 (1983), 144-164.
· The diophantine equation x3 + 3y3 = 2n , J.Number Th. 15 (1982), 376-387.