Unpublished notes

  1. Hilbert's inequality (pdf)
  2. The Byrnes-Gauger theorem (pdf)
  3. The Generalized 3x+1 (Collatz) Mapping (pdf)
  4. An inequality for the determinant of a positive definite Hermitian matrix (pdf)
  5. Short solutions of AX=B using a LLL-based Hermite normal form algorithm (pdf)
  6. Generalised eigenspaces and the block upper triangular form (pdf)
  7. Short multipliers for the extended gcd problem (pdf )
  8. A divisibility property of the continued fraction of a quadratic irrational - joint with John Robertson (pdf)
  9. On the LCM of n positive integers, J. Campbell (written up by K.R. Matthews) (pdf)
  10. Some continued fraction identities (pdf)
  11. Primitive Pythagorean triples and the negative Pell equation (pdf)
  12. On the continued fraction expansion of √22n+1 (pdf)
  13. A unimodular matrix and Pell's equation (pdf)
  14. Reduced quadratic irrationals and Pell's equation (pdf)
  15. Solving Ax2 - By2 = N in integers, where A > 0, B > 0 and D = AB is not a perfect square and gcd(A,B) = gcd(A,N) = 1 (pdf)
  16. A nearest integer formula for [x/m], x real, m a non=zero integer (pdf)

Last modified 9th October 2007