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1. (1 points)
N =

2. (12 points) Please complete the following multiplication table for Z7 (multiplication mod 7).
× 0 1 2 3 4 5 6
0 0 0 0 0 0 0 0
1 0 1 2 4 6

2 0 2 6 3 5

3 0 6 5 4

4 0 4 5 2 6

5 0 5 3 4 2

6 0 6 5 4 2 1
3. (12 points) Please complete the following proof that the prime numbers (P) are countably infinite.
Proof (Contradiction):
Suppose that the primes are finite, that is, suppose that P = {p1,p2,…,pn} for some finite n ∈Z+.