1. How many closed necklaces of length 7 can be made with 3 colors?
(notice that 7 is a prime)
2. How many closed necklaces of length 10 can be made with 3 colors
(this is di erent because 10 is not a prime: you need to think about
necklaces all of one color, necklaces with 5 repeating blocks of 2 colors,
necklaces with 2 repeating blocks of 5 colors, and necklaces with no
repeating pattern of length shorter than 10)?
3. Compute 834256743 mod 13 with the help of Fermat''s little theorem. Show
all work (I need to see how you used the theorem).
4. Determine (21). Use this information to compute 91000000000 mod 21
using Euler''s theorem.