Personal Description
Information about my teaching and research including publications may be found at my personal web site: http://www.math.waikato.ac.nz/~kab.

Research Interests
Number theory; mathematical software; computer algebra; optimisation; dynamical systems.

Publications - 2012

Articles in Refereed Journals

Broughan, Kevin A., De Koninck, J.M., Katai, I. and Luca, Florian (2012) On Integers for Which the Sum of Divisors is the Square of the Squarefree Core Jnl of Integer Sequences 15, Article 12.7.5.

Publications - 2011

Articles in Refereed Journals

Balog, Antal, Broughan, Kevin A. and Shparlinski, Igor E. (2011) On the number of solutions of exponential congruences Acta Arith. 148, 1-7.

Broughan, K.A. and Barnett, A.R. (2011) Gram lines and the average of the real part of the Riemann zeta function Maths of Computation doi: S0025-5718 02565-2, 1-11.

Broughan, Kevin A., Gonzalez, Marcos J., Ryan, H. Lewis, Luca, Florian, Huguet, V. Janitzio Mejia, Togbe, Alain (2011) There are no Multiply-perfect Fibonacci numbers Integers 11A, Article 7, 1-33.

Publications - 2010

Articles in Refereed Journals

Broughan, Kevin A. and Luca, Florian (2010) On the Fürstenberg closure of a class of binary recurrences Jnl of Number Theory v130, no3, Elsevier, 696-706.

Broughan, Kevin A. and Zhou, Qizhi (2010) Divisibility by 3 of Even Multiperfect Numbers of Abundancy 3 and 4 Jnl of Integer Sequences 13, Article 10.1.5.

Broughan, Kevin A., Luca, Florian and Shparlinski, Egor E. (2010) Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenhome's Theorem Integers 10, 485-495.

Publications - 2009

Abstracts of Conference Papers

Broughan, K.A. (2009) Flat Primes and Thin Primes 1047th AMS Meeting, University of Illinois, Urbana-Champaign.

Broughan, K.A. (2009) Gram lines and the average of the real part of the Riemann zeta function 1047th AMS Meeting, University of Illinois, Urbana-Champaign.

Articles in Refereed Journals

Broughan, K.A. (2009) An algorithm for the explicit evaluation of GL(n, R) Kloosterman sums ACM Comm in Comp Algebra 43, No. 1.

Broughan, K.A. (2009) Extension of the Riemann ξ-Function's Logarithmic Derivative Positivity Region to Near the Critical Strip Canad. Math. Bull. 52(2), pp.186-194.

Broughan, K.A. and Barnett, A. Ross (2009) On the missing values of n! mod p J. Ramanujan Math. Soc. 24, No. 3, 277-284.

Broughan, K.A. and Barnett, A.R. (2009) On the Subsequence of Primes Having Prime Subscripts Jnl of Integer Sequences 12, Article 09.2.3.

Broughan, Kevin A. and Zhou, Qizhi (2009) Flat Primes and Thin Primes Bull. Aust. Math. Soc. 82, 282-292.

Byard, Kevin and Broughan, Kevin (2009) Qualified difference sets from unions of Cyclotomic classes Bull. Aust. Math. Soc. 80, 147-158.