While I am at it, the final is on the first day of exam week, Friday the 10th. I hope to have some practice problems posted to the web by Friday afternoon for you to play with. E4.1-9 Let k be any positive integer. Since there is no class on Friday, more problem will be assigned tomorrow. Prove that exactly half of the nonzero elements of Z p are squares.
S be the set of nonzero elements of Z p which are squares.
Note this set will have some elements listed more than once. Show that if b is a nonzero element of Z p , then b and -b are not congruent modulo p . Give a counterexample to demonstrate that the statement does not hold when p and q are not relatively primes. Find one type I and one type II witness to the nonprimality of 35. Prove yourself each statement proved in the class.