Unpublished notes

  1. Hilbert's inequality (pdf)
  2. The Byrnes-Gauger theorem (pdf)
  3. An inequality for the determinant of a positive definite Hermitian matrix (pdf)
  4. Short solutions of AX=B using a LLL-based Hermite normal form algorithm (pdf)
  5. Generalised eigenspaces and the block upper triangular form (pdf)
  6. Short multipliers for the extended gcd problem (pdf )
  7. On the LCM of n positive integers, John Campbell (written up by K.R. Matthews) (pdf)
  8. Some continued fraction identities associated with √D (pdf)
  9. Primitive Pythagorean triples and the negative Pell equation (pdf)
  10. On the continued fraction expansion of √22n+1 (pdf)
  11. A unimodular matrix and Pell's equation (pdf)
  12. Reduced quadratic irrationals and Pell's equation (pdf)
  13. Solving Ax2 - By2 = N in integers, where A > 0, B > 0, N ≠ 0 and D = AB is not a perfect square and gcd(A,B) = gcd(A,N) = 1 (pdf)
  14. A nearest integer formula for [x/m], x real, m a non-zero integer (pdf)
  15. On the definition of nearest integer reduced quadratic surd (with John Robertson).
  16. A class of generalized 3x+1 mappings of Benoit Cloitre (pdf)
  17. An extension of the Hermite-Serret algorithm (pdf) (updated 1st October 2012)
  18. Solving the generalised Pell equation ax2-by2=±1
  19. Pseudocode for finding the shortest multipliers for the extended gcd problem (18th August 2011)
  20. Some remarks about the solutions of x2-Dy2=±N
  21. A note on the Markoff numbers conjecture (last modified 5th November 2013)
  22. On a transformation of Lagrange
  23. An equivalent form of the Dujella unicity conjecture
  24. Geometric nature of an equivalence class for the diophantine equation x2 – Dy2 = N, D > 0 and non square, N > 0
  25. Geometric nature of an equivalence class for the diophantine equation x2 – Dy2 = N, D > 0 and non square, N < 0
  26. Intermediate convergents
  27. On Markov's doubly-infinite sequence of forms
  28. On the continued fractions of conjugate quadratic irrationalities

Last modified 10th July 2017