Elementary Number Theory

Problem Set # 12

On the problem set, there are 3 points per problem. You have to have it all right to get all 3 points. A little tiny bit wrong and you get 2 points. A little bit right and you get 1 point. All wrong is 0.

Section 10.2

1, note that you must compute S(n) for certain values of n in order to "construct" this answer. It is easy enough to see that 29 = 2^2 + 5^2 (= 4 + 25). So, you know something about the answer, but you have to compute it. It is enough to find S(1) and then you have to figure out what el to use and compute it as well. You might know that (S(1)/2)^2 has to be 4 or 25, but you have to compute S(1) to see if it is plus or minus 4 or plus or minus 10. There are shortcuts, but they aren't that short.

Section 10.2

3

for p=5, 7, 11, 13.

Your last problem set! It must be turned in May 2. Late homework will not be accepted.