Macquarie University, Sydney Macquarie University ResearchOnline

Showing items 1 - 15 of 70.

Add to Quick Collection   All 70 Results

Sort:
 Add All Items to Quick Collection
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195102
Description: We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduc ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1055140
Description: Given a function f in a finite field Fq of q elements, we define the functional graph of f as a directed graph on q nodes labelled by the elements of Fq where there is an edge from u to v if and only ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1200625
Description: 28 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332383
Description: We give an upper bound for the number of elliptic Carmichael numbers η ≤ χ that were recently introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non CM). We ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/305892
Description: 8 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221888
Description: 8 page(s)
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/195607
Description: We give upper and lower bounds on the count of positive integers n <= x dividing the nth term of a non-degenerate linearly recurrent sequence with simple roots.
Full Text: Full Text
Reviewed: Reviewed
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/176439
Description: We recall that a polynomial f(X)= K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) = ℤ[X] are stable over ℚ. We ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/172505
Description: We give an upper bound on the number of finite fields over which elliptic curves of cryptographic interest with a given embedding degree and small complex multiplication discriminant may exist, and pr ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2011
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/136401
Description: We give asymptotic formulas for the number of biquadratic extensions of ℚ that admit a quadratic extension which is a Galois extension of ℚ with a prescribed Galois group, for example, with a Galois g ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2011
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/134834
Description: Aigner has defined elite primes as primes p such that all but finitely many of Fermat numbers F(n) = 2²ⁿ + 1, n = 0, 1, 2..., are quadratic nonresidues modulo p. Since the sequence of Fermat numbers i ... More
Reviewed: Reviewed
Date: 2011
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/146331
Description: 11 page(s)
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128904
Description: 9 page(s)
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129168
Description: Let g ≥ 2 be an integer and let (u n ) n≥1 be a sequence of integers which satisfies a relation u n+1 = h(n)u n for a rational function h(X). For example, various combinatorial numbers as well as thei ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128917
Description: We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets ... More
Reviewed: Reviewed