## Unpublished notes

- Hilbert's inequality (pdf)
- The Byrnes-Gauger theorem (pdf) (replace line -1 on page 2 by correction)
- An inequality for the determinant of a positive definite Hermitian matrix (pdf)
- Short solutions of AX=B using a LLL-based Hermite normal form algorithm (pdf)
- Generalised eigenspaces and the block upper triangular form (pdf)
- Short multipliers for the extended gcd problem (pdf )
- On the LCM of n positive integers, John Campbell (written up by K.R. Matthews) (pdf)
- Some continued fraction identities associated with √D (pdf)
- Primitive Pythagorean triples and the negative Pell equation (pdf)
- On the continued fraction expansion of √2
^{2n+1} (pdf)
- A unimodular matrix and Pell's equation (pdf)
- Reduced quadratic irrationals and Pell's equation (pdf)
- Solving Ax
^{2} - By^{2} = 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)
- A nearest integer formula for [x/m], x real, m a non-zero integer (pdf)
- On the definition of nearest integer reduced quadratic surd (with John Robertson).

- A class of generalized 3x+1 mappings of Benoit Cloitre (pdf)
- An extension of the Hermite-Serret algorithm (pdf) (updated 1st October 2012)
- Solving the generalised Pell equation ax
^{2}-by^{2}=±1
- Pseudocode for finding the shortest multipliers for the extended gcd problem (18th August 2011)
- Some remarks about the solutions of x
^{2}-Dy^{2}=±N
- A note on the Markoff numbers conjecture (last modified 5th November 2013)
- On a transformation of Lagrange
- An equivalent form of the Dujella unicity conjecture
- Geometric nature of an equivalence class for the diophantine equation x
^{2} – Dy^{2} = N, D > 0 and non square, N > 0
- Geometric nature of an equivalence class for the diophantine equation x
^{2} – Dy^{2} = N, D > 0 and non square, N < 0
- Intermediate convergents
- On Markov's doubly-infinite sequence of forms
- On the continued fractions of conjugate quadratic irrationalities

*Last modified 18th January 2019*