12,289 research outputs found
Square-full primitive roots
We use character sum estimates to give a bound on the least square-full
primitive root modulo a prime. Specifically, we show that there is a
square-full primitive root mod less than , and we give some conditional bounds.Comment: 9 page
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
-adic quotient sets
For , the question of when is dense in the positive real numbers has been examined by
many authors over the years. In contrast, the -adic setting is largely
unexplored. We investigate conditions under which is dense in the
-adic numbers. Techniques from elementary, algebraic, and analytic number
theory are employed in this endeavor. We also pose many open questions that
should be of general interest.Comment: 24 page
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