Vijay N. – BASIS Scottsdale

BASIS Scottsdale Senior Vijay N.

Don't be a Square: Magic Square of Squares

Project/blog link: Don't be a Square: Magic Square of Squares
BASIS Advisor: Ms. Marizza Bailey
Internship location: ASU, School of Mathematical and Statistical Sciences
Onsite Mentor: Dr. John Jones, Professor

Project Abstract

Have you ever wondered if squares are magical? A magic square is an array of numbers in which the columns, rows and diagonals add up to the same number. Mathematicians have wondered if it is possible to make a “3-by-3 magic square of squares,” a 3-by-3 magic square where the number in each box is the square of an integer. Working within the math department at Arizona State University, I will be researching the properties that would need to be satisfied by such a magic square, thereby identifying whether such a magic square could exist. It might be possible to prove that a magic square exists by trying to generate one. Or, it might be possible to prove that a magic square of squares cannot exist by “modding out” entries to see what arrangements of entries are not possible. This is certainly a very difficult problem; mathematicians have worked on this problem for quite a long time and have still not solved it. Although the problem has yet to be solved, mathematicians have made progress by finding necessary conditions for such a square. I will be using number theory, and in particular, modular arithmetic to find more necessary problems and using computer programs to generate similar magic squares. Number theoretic results have applications to cryptography and coding theory, allowing data to pass safely through the internet without being confiscated.

Don't be a Square: Magic Square of Squares