6 research outputs found
A proof of the conjecture of Cohen and Mullen on sums of primitive roots
We prove that for all , every non-zero element in the finite field
can be written as a linear combination of two primitive roots
of . This resolves a conjecture posed by Cohen and Mullen.Comment: 8 pages; to appear in Mathematics of Computatio
The combinatorics of binary arrays
This paper gives an account of the combinatorics of binary arrays, mainly concerning their randomness properties. In many cases the problem reduces to the investigation on difference sets.postprin
Artin's primitive root conjecture -a survey -
This is an expanded version of a write-up of a talk given in the fall of 2000
in Oberwolfach. A large part of it is intended to be understandable by
non-number theorists with a mathematical background. The talk covered some of
the history, results and ideas connected with Artin's celebrated primitive root
conjecture dating from 1927. In the update several new results established
after 2000 are also discussed.Comment: 87 pages, 512 references, to appear in Integer