# Homework 5

Due Wednesday, November 15:

1. Section 4.1 (page 244) #9
2. Section 4.1 (page 245) # 28
3. Compute the following:
• 13569 mod 3
• 13569 mod 5
• $6^{20}$ mod 11
4. Convert the following numbers from decimal to binary:
• 111
• 127
• 128

Challenge: (Optional) Let a, b and c be any integers, and n > 1. Show that if $a \equiv b$ (mod n) and $b \equiv c$ (mod n), then $a \equiv c$ (mod n).