Department Of Mathematics

Publications of Nikos Tzanakis

List of Publications:

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

2. On the diophantine equation y2 - D = 2k , J.Number Th.17 (1983), 144-164.

3. (In cooperation with A.Bremner) Integer points on y2 = x3 - 7x + 10, Math.Comp. 41 (1983), 731-741.

4. The diophantine equation x3 - 3xy2 - y3 = 1 and related equations, J .Number Th. 18 (1984), 192-205.

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

6. On the diophantine equation 2x3 + 1 = py2 , Manuscr. Math. 54 (1985), 145-164.

7. A remark on a theorem of W.E.H.Berwick, Math. Comp. 46 (1986), 623-625.

8. On the diophantine equation x2 - Dy4 = k , Acta Arithm. 46 (1986), 257-269.

9. (In cooperation with J.Wolfskill) On the diophantine equation y2 = 4qn + 4q + 1 , J. Number Th. 23 (1986)219-237.

10. (In cooperation with J.Wolfskill) The diophantine equation y2 = 4qa/2 + 4q + 1 with an application to Coding Theory, J. Number Th. 26 (1987), 96-116.

11. (In cooperation 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.

12. (In cooperation with B.M.M. de Weger) On the practical solution of the Thue equation,
    J.Number Th. 31 (1989), 99-132.

13. On the practical solution of the Thue equation-an outline, Colloqu. Math. Soc. Janos Bolyai
    51 (1987), 1003-1012.

14. (In cooperation with R.P.Steiner) Simplifying the solution of Ljunggren's equation x2 + 1 = 2y4,
    J. Number Th. 37 (1991), 123-132.

15. (In cooperation with J.Buchmann,K.Gy'o'ry,M.Mignotte) Lower bounds for P( x3 + k ) , an elementary approach , Publ. Math. Debrecen 38/1-2 (1991), 145-163.

16. (In cooperation with M.Mignotte) Arithmetical study of recurrence sequences, Acta Arithm. 57 (1991), 357-364.

17. (In cooperation with M.Mignotte) On a family of cubics, J.Number Th. 39 (1991),41-49.

18. (In cooperation with B.M.M.de Weger) Solving a specific Thue-Mahler equation, Math.Comp. 57 (1991), 799-815.

19. (In cooperation 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.

20. (In cooperation with B.M.M.de Weger) How to explicitly solve a Thue-Mahler equation,
    Compos. Math. 84 (1992), 223-288.

21. (In cooperation with M.Mignotte) Arithmetical study of a certain ternary recurrence sequence
    and related equations, Math.Comp. 61 (1993), 901-913.

22. Explicit solution of a class of quartic Thue equations, Acta Arithm. 64 (1993), 271-283.
    (In cooperation with R.J.Stroeker) Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms, Acta Arithm. 67 (1994), 177-196.

23. Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms.
    The quartic case., Acta Arithm. 75 (1996), 165-190.

24. (In cooperation with A. Bremner and R .J. Stroeker) On sums of consecutive squares,
    J.Number Th. 62 (1997), 39-70.

25. (In cooperation with R.J.Stroeker) On the elliptic logarithm method for elliptic diophantine
    equations: Reflections and an improvement, Experimental Math. (to appear).