Browsing University of Waterloo by Author "Murty, M. Ram"
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A lower bound for the two-variable Artin conjecture and prime divisors of recurrence sequences
Murty, M. Ram; Séguin, François; Stewart, Cameron L. (Elsevier, 2019-01-01)In 1927, Artin conjectured that any integer other than −1 or a perfect square generates the multiplicative group (Z/pZ)× for infinitely many p. In 2000, Moree and Stevenhagen considered a two-variable version of this ... -
Sieve methods in combinatorics
Liu, Yu-Ru; Murty, M. Ram (Elsevier, 2005-07)We develop the Turán sieve and a ‘simple sieve’ in the context of bipartite graphs and apply them to various problems in combinatorics. More precisely, we provide applications in the cases of characters of abelian groups, ... -
A weighted Turán sieve method
Liu, Yu-Ru; Murty, M. Ram (Elsevier, 2006-01)We develop a weighted Turán sieve method and applied it to study the number of distinct prime divisors of f (p) where p is a prime and f (x) a polynomial with integer coefficients.