Math 511 Exam 1
October 2, 2000
1. Find the (multiplicative) inverse of 43 (mod 142).
2. Factor 261,257 given 5792 º 2722 (mod 261,257).
3. Find examples of quadratic equations (mod 35) with
a. No roots
b. 2 roots
c. 4 roots
4. Prove that -1 ´ -1 = 1 in any field.
5. Explain how and why the RSA public key encryption system works, in a manner suitable for an audience of bright high school students. You may assume the audience is familiar with modular arithmetic. Your explanation will be graded on both correctness and clarity (which includes grammar and spelling).
On my honor as a student, I have neither given nor received unauthorized aid on this academic work.
____________________________________ ______________
(signature) (date)