Modular arithmetic of fractions, divisibility tests, and beyond
Time and place
12:45–1:45 PM on Thursday, June 30th, 2022; MR1
Jay Jorgenson (CCNY)
Abstract
In this talk, we will show that one has a consistent notion of fractions in the setting of modular arithmetic, and that many divisibility tests can be viewed as computing 1/10 in different number systems. We will discuss, as is known, that the effectiveness of the RSA algorithm stems from the complexity associated to the problem of computing 1/a mod m for known a but unknown m. Finally, we will challenge the notion of "complexity" by asking "to whom, using what", which introduces the potential usefulness of quantum (or other) computers.
