Assignment 6

1. Prove by contradiction that: there are no integers a and b for which 18a+6b = 1.

2. Prove by contradiction that:

if a,b Z, then a2 4b = 2

3. Prove by contrapositive that: If x and y are two integers whose product is even, then at least one of the two must be even.

Make sure that you clearly state the contrapositive of the above statement at the beginning of your proof.

4. Prove that for all integers x, x2 + 5x - 1 is odd.