Math 5248 Lec 2 Homework 3 Due Thursday March 7
Five questions, 20 points each.
I. Find all square roots of 4 modulo 5•7•11. A direct search which does not use the methods of
this course gets no credit. If you find all the roots, you get 20 points; otherwise you get one point
per square root (assuming you are using an acceptable method).
II. Apply the Fermat test to n =8388607 and m = 8388609. That is, compute 2n-1 mod n and 2m-1
mod m (4pts) You can use the fast exponentiation spreadsheet if you wish. Using this test, what
can we say about the primality of these numbers? Be sure to explain your answer. (16 pts)
10.5.2
13.6.5
18.1.2