On some Quadratic Diophantine Equations And Semiperfect Numbers

Abstract

A Master of Science in Mathematics by Imane Sahel entitled, “On some Quadratic Diophantine Equations and Semiperfect Numbers”, submitted in April 2025. Thesis advisor is Dr. Abdel Rahman Yousef and thesis co-advisor is Dr. Issam Louhichi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).This thesis investigates quadratic Diophantine equations of the form χ^α + y² = z² and explores properties of semiperfect and weird numbers. We derive explicit formulas for the number of integer solutions when χ^α is a perfect square and when it is not. Using these results, we make some observations about odd and even perfect numbers. The second part examines sum of divisor based number classifications; we study abundant, semiperfect and primitive weird numbers.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH