(1 and 2 are just for fun and nothing to do with Class #8 per se)
1. What is the prime factorization of 1,005,010,010,005,001 ?
2. Simplify 33334444 + 44443333 mod 7
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3. For the first two subgroups of Z19 , Group 1 and Group 2, see if you can find generators for them.
4. Consider the complex number set { 1,1,i,i, } together with
ordinary multiplication is a group.
a) Can you identify a subgroup of it?
b) Can you identify a generator for it?
1 1
5. Consider the matrix . I claim you can produce a group using it as a generator. See
what you can find out.
i/6
6. I claim you can use the complex number e as a generator for a group, together with ordinary multiplication. See what you can find out.
7. What size subgroups would you expect Z41 to have ?
8. Try Fermat’s Factorization method out on 5293.
