CMPSCI 250: Introduction to Computation

David Mix Barrington

Fall, 2004

Question and Answers on HW#3

Due on paper in class, Wednesday 13 October 2004

Questions are in black, answers in blue

Question #2, 12 Oct 2004

Is there a mistake in the extra credit problem? When I try p=3, I get (p-1)! = 2 but (-1)^{(p-1)/2} = -1. But these numbers are supposed to be equal...

My mistake, I should have said "congruent to modulo p" rather than "equal to". I agree that 2 and -1 are not equal, but they are congruent modulo 3. The problem is correctly stated once this is fixed. Sorry!

Question #1, 12 Oct 2004

I'm having trouble proving 2.9.3 -- in fact I don't think it's true! I think I have an example of an A, B, f, and g such that g composed with f is a bijection but neither f nor g is a bijection.

You're quite right, I screwed up. The statement I asked you to prove is false. For full credit, give an example where g composed with f is a bijection but either f or g (or both) is not.

Last modified 12 October 2004