Artin’s Primitive Root Conjecture represents one of many famous problems in elementary number theory that has resisted complete solution thus far. Significant progress was made in 1967, when Christopher Hooley published a conditional proof of the conjecture under the assumption of a certain case of the Generalised Riemann Hypothesis. In this survey we present a description of the conjecture and the underlying algebraic theory, and provide a detailed account of Hooley’s proof which is intended to be accessible to those with only undergraduate level knowledge. We also discuss a result concerning the qx+1 problem, whose proof requires similar techniques to those used by Hooley.
Samuel Le Fourn
"A Case Study on Hooley's Conditional Proof of Artin's Primitive Root Conjecture,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 21
, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss2/3