- 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 \(\lfloor x/m\rfloor\), x real, m a non-zero integer (pdf)
- On the definition of nearest integer reduced quadratic surd (with John Robertson).

- Converting the regular continued fraction of √D to the nearest integer continued fraction
- 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 for solving ax
^{2}+ bxy + cy^{2}= n, where b^{2}– 4ac < 0 - 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
- Solving the Diophantine equation ax
^{2}+ bxy + cy^{2}+ dx + ey + f = 0, (last modified 29th August 2022) - Hardy and Wright Theorem 172 when PS – QR = ±4 instead of ±1 (13th August 2016)
- On the convergents of semi-regular continued fractions (revised 25th November 2010)
- Converting the regular continued fraction of √D to the nearest integer continued fraction
- Continuants and semi-regular continued fractions (Alan Offer)
- Period two NSCF and NICF expansions of √D (23rd April 2009).
- Finding the Stolt fundamental solutions of ax
^{2}+ bxy + cy^{2}= N. (5th August 2021)

*Last modified 27th September 2023*