 
Summary: Math 3130 Final: Due
Thursday December 16th, 4pm
Remember to show your work!
Directions This is a take home, open notes
test. There are three sections. You must
answer carefully at least six problems with
at least one from each section. You answer
must be your own; you are free to discuss
problems with other students but must write
up your own answers. Excessive similarity of
answers will be noted and dealt with appro
priately.
I) Foundations and the Integers
Problem 1 Using the Euclidean algorithm
and showing the steps, find the multiplicative
inverse of 125 modulo 364.
Problem 2 Suppose that f(x) Zp[X], p
odd, is a quadratic polynomial. Prove in gen
eral that the polynomial function from Zp to
itself obtained by evaluating f(x) cannot be
