# 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