MA 1971 Bridge to Higher Mathematics
Quiz 3
Show all work needed to reach your answers.
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
+.
