56 citations · 78 across the 13 of their papers we have counts for
5 papers · 1 filter
The great trinomial hunt
Richard P. Brent, Paul Zimmermann
We describe a search for primitive trinomials of high degree and its interaction with the Great Internet Mersenne prime search (GIMPS). The search is complete for trinomials whose…
On computing factors of cyclotomic polynomials
Richard P. Brent
For odd square-free n > 1 the n-th cyclotomic polynomial satisfies an identity of Gauss. There are similar identity of Aurifeuille, Le Lasseur and Lucas. These identities all invol…
On the periods of generalized Fibonacci recurrences
Richard P. Brent
We give a simple condition for a linear recurrence (mod 2^w) of degree r to have the maximal possible period 2^(w-1).(2^r-1). It follows that the period is maximal in the cases of…
Some integer factorization algorithms using elliptic curves
Richard P. Brent
Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algor…
Factorizations of Cunningham numbers with bases 13 to 99
Richard P. Brent, Peter L. Montgomery, Herman J. J. te Riele
This Report updates the tables of factorizations of a^n +- 1 for 13 < a < 100, previously published as CWI Report NM-R9212 (June 1992) and updated in CWI Report NM-R9419 (Update 1,…