Download Math 142 Writing Proofs about Numbers Spring 2013 If m is divisible

Math 142
Writing Proofs about Numbers
Spring 2013
1. If m is divisible by 4 and n is any even integer, then m n is divisible by 8.
Proof:
2. If n 2 is even, then n is even. (HINT: Use an indirect proof).
Proof:
3. If 3 divides b and b divides c, then 3 divides c. (HINT: Be careful with your
substitution step).
Proof:
4. For any rational number r, the number r + 2 is also rational.
Proof:
5. Prove that if n is odd, the sum of itself and its square is even.
Proof:
6. Prove using an indirect proof, the following:
If m + n is odd, then m or n must be even.
Proof:
7. For any integer n, n + 3n is always even. (HINT: Use both cases for n, when n is
even and when n is odd).
Proof:
8. Compute each of the following.
a. 73 mod 6 =
b. 187 mod 11 =
c. 55 mod 6 =
d. 6 mod 55 =
e. 12 mod 5