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Homework #8 MME 529 SOLVED

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Homework #8 MME 529
(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
___________________________________________
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 }
2
( 1 )
,
2
( 1 )
,
2
(1 )
,
2
(1 )
{ 1, 1, , ,
i i i i
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?
5. Consider the matrix 










 
2
1
2
1
2
1
2
1
. I claim you can produce a group using it as a generator. See
what you can find out.
6. I claim you can use the complex number
i / 6
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.

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