[Solved] MME529 Homework #8

(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.

1. Can you identify a subgroup of it?
2. 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 Fermats Factorization method out on 5293.