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 + 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 px² + q²ⁿ= 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 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 + 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  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 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( 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 equation,  J.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 = 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 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 = 2^k , J.Number Theory 17 (1983), 144-164.

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