Chapter 12

 

Exercise 6. This software determines the number of solutions to the equation X2 = -I where X is a 2 x 2 matrix with entries from Zn and I is the identity. Run the program for n = 32. Make a conjecture about the number of solutions when n = 2k where k > 1. Run the program for n = 3, 11, 19, 23, and 31 . Make a conjecture about the number of solutions when n is a prime of the form 4q + 3. Run the program for n = 27 and 49. Make a conjecture about the number of solutions when n has the form pi where p is a prime of the form 4q + 3. Run the program for n = 5, 13, 17, 29, and 37. Make a conjecture about the number of solutions when n is a prime of the form 4q + 1. Run the program for n = 6, 10, 14, 22; 15, 21, 33, 39; 30, 42. What seems to be the relationship between the number of solutions for a given n and the number of solutions for the prime power factors of n ?  

 Making of the project / Project Home Page / UMD Undergraduate Math Program