Date of Award
5-2018
Document Type
Thesis
Degree Name
Master of Science (MS)
College/School
College of Science and Mathematics
Department/Program
Mathematical Sciences
Thesis Sponsor/Dissertation Chair/Project Chair
Aihua Li
Committee Member
Baojun Song
Committee Member
Bogdan G. Nita
Abstract
This work is dedicated to the properties of the 3 × 3 magic squares of cubes modulo a prime number. Its central concept is the number of distinct entries of these squares and the properties associated with this number. We call this number the degree of a magic square. The necessary conditions for the magic square of cubes with degrees 3, 5, 7, and 9 are examined. It was established that there are infinitely many primes for which magic squares of cubes with degrees 3, 5, 7, and 9 exist. I apply n-tuples of consecutive cubic residues to prove that there are infinitely many Magic Squares of Cubes with degree 9. Furthermore I use Brauer’s theorem, that guarantees the existence of a sequence of consecutive integers of any length, to construct Magic Squares of Cubes whose entries are all cubic residues. Such analytic tools as Modular Arithmetic, Legendre symbol, Fermat’s Little Theorem, notions of quadratic and cubic residues were employed in the process of research.
Recommended Citation
Sokolovskiy, Yevgeniy, "Magic Squares of Cubes Modulo a Prime Number" (2018). Theses, Dissertations and Culminating Projects. 152.
https://digitalcommons.montclair.edu/etd/152