Nikos (Nikolaos) G. Tzanakis - Research Publications

(with G. Soydan), Complete solution of the Diophantine equation x2 + 5a 11b = 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 px2 + q2n= yp 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 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 Th62 (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 logarithmsActa 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( 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 equationJ.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.


 


Last update: 9 March 2017