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TOPICS IN DIVISIBILITY: PAIRWISE COPRIMALITY, THE GCD OF SHIFTED SETS AND POLYNOMIAL IRREDUCIBILITY

Published online by Cambridge University Press:  02 January 2016

RANDELL HEYMAN*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia email randell@unsw.edu.au
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Abstract

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Type
Abstracts of Australasian PhD Theses
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Akiyama, S. and Pethő, A., ‘On the distribution of polynomials with bounded roots II. Polynomials with integer coefficients’, Unif. Distrib. Theory 9(1) (2014), 519.Google Scholar
Dietmann, R., ‘On the distribution of Galois groups’, Mathematika 58 (2012), 3544.CrossRefGoogle Scholar
Ding, C., Pei, D. and Salomaa, A., The Chinese Remainder Theorem (World Scientific, Singapore, 1996).CrossRefGoogle Scholar
Gauss, C. F., Disquisitiones Arithmeticae, English edn (Springer, New York, 1986).CrossRefGoogle Scholar
Heyman, R., ‘Pairwise non-coprimality of triples’, Preprint, 2014, arXiv:1309.5578 [math.NT].Google Scholar
Hu, J., ‘Pairwise relative primality of positive integers’, Preprint, 2014, arXiv:1406.3113 [math.NT].Google Scholar
Katz, V. J., A History of Mathematics, brief edn (Pearson/Addison-Wesley, Boston, MA, 2003).Google Scholar
Knuth, D. E., The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, 3rd edn (Addison-Wesley, Boston, MA, 1998).Google Scholar
Lenstra, A. K., Lenstra, H. W. and Lovász, L., ‘Factoring polynomials with rational coefficients’, Math. Ann. 261 (1982), 515534.CrossRefGoogle Scholar
Moree, P., ‘Counting carefree couples’, Math. News. 24(4) (2014), 103110.Google Scholar
Zywina, D., ‘Hilbert’s irreducibility theorem and the larger sieve’, Preprint, 2010, arXiv:1011.6465 [math.NT].Google Scholar