University Calendar

Nicholas Ryan Bilynsky presents his Master's Thesis Defense.

Abstract

A magic square is a square table of numbers such that each row, column, or diagonal adds up to the same sum. This research is inspired by an open question posed by Martin Labar in 1984. The open question states: “Can a 3x3 magic square be constructed using nine distinct perfect squares?" For over two thousand years, many mathematicians have looked at these magical properties. In this thesis, the focus is on certain prime numbers p. We show that there exist Magic Squares of Squares with nine distinct elements modulo p, for infinitely many prime numbers. Constructions of such magic squares of squares are given. Results from this research provide a positive answer to a similar question regarding integers modulo certain prime numbers.