As a consequence of Algorithm 1 below, there always exist integers x, y ∈ Z such that ax+by = gcd(a, b). We say that a and b are co-prime (or relatively prime) if gcd(a, b) = 1, i.e., ax = 1 mod b. From this, x is the multiplicative inverse of a modulo b, and likewise y is the multiplicative inverse of b modulo a. The following deterministic algorithm shows that gcd(a, b) (and additionally, the...

Seven new appointments and six returns from leaves of absence were included in the announcement of faculty changes released yesterday by Dr. John M. Sayles, acting president of the college. Heading this listing of changes was the appointment of Dr. Sayles as successor to the late Dr. A. R. Brubacher as president of the college. Formerly director of training and principal of Milne, Dr. Sayles wi...

Instructor, Department of Internal Medicine, University of Texas Southwestern Medical Center and Dallas VA Medical Center, Esophageal Diseases Center, Dallas, Texas 75216, USA *Corresponding author Xiaofang Huo, MD, PhD Instructor Department of Internal Medicine University of Texas Southwestern Medical Center and Dallas VA Medical Center, Esophageal Diseases Center Dallas, Texas 75216, USA E-ma...

Instructional content designers of online learning platforms are concerned about optimal video design guidelines that ensure course effectiveness, while keeping video production time and costs at reasonable levels. In order to address the concern, we use clickstream data from one Coursera course to analyze the engagement, motivational and navigational patterns of learners upon being presented w...