Artin's Conjecture and Patterns in Long Division by Prof. Leo Goldmakher, Williams College

Artin’s Conjecture and Patterns in Long Division by Prof. Leo Goldmakher, Williams College, Monday March 3, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: Using long division, we find that 1/7 = 0.142857142857142857…, 1/11 = 0.0909090909…, 1/13 = 0.076923076923076923…, etc.. These decimals may look random, but they contain a lot of secret structure—some proved, some observed but still open. We’ll discuss some of this structure and connect these decimals to the structure of the multiplicative group of integers (mod p). This will lead us to Artin’s conjecture on primitive roots, a major open problem in number theory / group theory. I will conclude by discussing some very recent results refining Artin’s conjecture, discovered jointly with Greg Martin and Paul Péringuey (both at UBC).