Personal Page
Book Chapter
Matthews, Keith R. (2010). Generalized 3x+1 mappings: Markov chains and ergodic theory. In Jeffrey C. Lagarias (Ed.), The ultimate challenge: The 3x+1 problem (pp. 79-103) Providence, RI, U.S.A.: American Mathematical Society.
Journal Articles
Matthews, Keith R. , Robertson, John P. and Srinivasan, Anitha (2017) Extending Theorems of Serret and Pavone. Journal of Integer Sequences, 20 10: 1-11.
Matthews, Keith R., Robertson, John P. and Srinivasan, Anitha (2015) On fundamental solutions of binary quadratic form equations. Acta Arithmetica, 169 3: 291-299. doi:10.4064/aa169-3-4
Matthews, Keith R. (2014) Lagrange's Algorithm Revisited: Solving at2 + btu + cu2 = n in the case of negative discriminant. Journal of Integer Sequences, 17 11: .
Matthews, Keith R., Robertson, John P. and White, Jim (2013) On a diophantine equation of Andrej Dujella. Glasnik Matematicki, 48 2: 265-289. doi:10.3336/gm.48.2.04
Matthews, Keith R. (2012) On the optimal continued fraction expansion of a quadratic surd. Journal of the Australian Mathematical Society, 93 1-2: 133-156. doi:10.1017/S1446788712000596
Matthews, Keith R. and Robertson, John P. (2011) Period-length equality for the nearest integer and nearest square continued fraction expansions of a quadratic surd. Glasnik Matematicki, 46 2: 269-282. doi:10.3336/gm.46.2.01
Matthews, Keith R. and Robertson, John P. (2010) Purely periodic nearest square continued fractions. Journal of Combinatorics and Number Theory, 2 3: 239-244.
Matthews, Keith, Robertson, John and White, Jim (2010) Midpoint criteria for solving Pell's equation using the nearest square continued fraction. Mathematics of Computation, 79 269: 485-499. doi:10.1090/S0025-5718-09-02286-8
Matthews, Keith R. (2009) Unisequences and nearest integer continued fraction midpoint criteria for Pell’s equation. Journal of Integer Sequences, 12 6: Article 09.6.7.
Robertson, John P. and Matthews, Keith R. (2008) A continued fractions approach to a result of Feit. American Mathematical Monthly, 115 4: 346-349.
Matthews, Keith R., Robertson, John P. and White, Jim (2008) Corrigenda to “Calculation of the regulator of Q(√D) by use of the nearest integer continued fraction algorithm”. Mathematics of Computation, 78 265: 615-616. doi:10.1090/S0025-5718-08-02142-X
Jackson, Terrence and Matthews, Keith (2002) On Shanks' algorithm for computing the continued fraction of log b a. Journal of Integer Sequences, 5 2.7: 1-9.
Matthews, K. (2002) The Diophantine equation ax2 + bxy + cy2 = N, D = b2 - 4ac > 0. Journal de Theorie des Nombres, 14 1: 257-270.
Matthews, K (2002) Thue's theorem and the diophantine equation x2 - Dy2 = ±N. Mathematics of Computation, 71 239: 1281-1286. doi:10.1090/S0025-5718-01-01381-3
Matthews, K. R. (2000) The diophantine equation x2 - Dy2 = N, D > 0. Expositiones Mathematicae, 18 323-331.
Havas, G, Majewski, BS and Matthews, KR (1999) Extended GCD and hermite normal form algorithms via lattice basis reduction (vol 7, pg 125, 1998). Experimental Mathematics, 8 205-205.
Havas, George, Majewski, Bohdan S. and Matthews, Keith R. (1998) Extended GCD and hermite normal form algorithms via lattice basis reduction. Experimental Mathematics, 7 2: 125-136. doi:10.1080/10586458.1998.10504362
Matthews K.R. (1996) Minimal multipliers for consecutive Fibonacci numbers. Acta Arithmetica, 75 3: 205-218.
Matthews, K.R and Leigh, G.M (1987) A generalization of the Syracuse algorithm in Fq[x]. Journal of Number Theory, 25 3: 274-278. doi:10.1016/0022-314X(87)90032-1
Matthews K.R. (1977) An example from power residues of the critical problem of Crapo and Rota. Journal of Number Theory, 9 2: 203-208. doi:10.1016/0022-314X(77)90023-3
Theses
Matthews, Keith Robert (1974). An investigation of the Davenport-Halberstam inequality and a generalization of Artin's conjecture for primitive roots PhD Thesis, School of Mathematics and Physics, The University of Queensland.
Matthews, Keith Robert. (1966). Waring's theorem for polynomials over a finite field M.Sc Thesis, School of Physical Sciences, The University of Queensland.