[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 Fermat’s Factorization method out on 5293.