Malik Muhammad Khurram Sher Khan, MD, Malik Muhammad Humayun Sher Khan, MD, Aaron Tolan, MD, Darryl Elmouchi, MD, FHRS, Carlos E. Tavera, MD, FACP From the Grand Rapids Medical Education Partners, Michigan State University, Grand Rapids, Michigan, Frederik Meijer Heart & Vascular Institute, Spectrum Health, Grand Rapids, Michigan, and Department of Internal Medicine, Michigan State University C...

Corresponding Author: Manar Abu Talib Department of Computer Science, University of Sharjah, P.O.Box 27272, Sharjah, UAE Email: [email protected] Abstract: Researchers, practitioners and social scientists all agree on the enormous importance of social science research in advancing human knowledge and informing public policy makers. The National Research Foundation, along with other organ...

In this paper, we study the existence of Diophantine quadruples with the property D(z) in the ring Z[ √−2 ]. We find several new polynomial formulas for Diophantine quadruples with the property D(a+ b √−2 ), for integers a and b satisfying certain congruence conditions. These formulas, together with previous results on this subject by Abu Muriefah, Al-Rashed and Franušić, allow us to almost com...