Nikos (Nikolaos) G. Tzanakis - Research Publications

(with P. Voutier),  Near-squares in binary recurrence sequences, (preprint)

(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 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 Arith. 152 (2012), 39-49.

(with A. Laradji, M. Mignotte), On px2 + q2n= yp 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 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 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  y2 = x(x2-n2), 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 logarithmsActa 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( 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 Theory 37 (1991), 123-132.

·        (with B.M.M. de Weger) On the practical solution of the Thue equationJ.Number Theory31 (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 y2 = 4qa/2 + 4q + 1 with an application to Coding Theory, J. Number Theory 26 (1987), 96-116.

·        (with J.Wolfskill) On the diophantine equation y2 = 4qn + 4q + 1 J. Number Theory 23, 219-237.

·        On the diophantine equation x2 - Dy4 = 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 2x3 + 1 = py2 , Manuscripta Math. 54 (1985), 145-164.

·        The complete solution in integers of x3 + 3y3 = 2n , J. Number Theory 19 (1984), 203-208.

·        The diophantine equation x3 - 3xy2 - y3 = 1 and related equations, J .Number Theory 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 Theory 17 (1983), 144-164.

·        The diophantine equation x3 + 3y3 = 2n , J.Number Theory 15 (1982), 376-387.

Last update: 24 August 2021