Guest User

Untitled

a guest
Jan 21st, 2018
99
0
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
text 0.55 KB | None | 0 0
  1. The generators for mod 13 are 2, 6, 7 and 11 because
  2. g^k is different for each k in 1...p-1
  3.  
  4.  
  5. ii. Compute φ(6), φ(10) and φ(12)
  6.  
  7. φ(6) 6: 2*3
  8. φ(6) = 6*(1-1/2)*(1–1/3)
  9. φ(6) = 2
  10.  
  11. φ(10) 10: 2*5
  12. φ(10) = 10 * (1 - ½) * (1 – 1/5)
  13. φ(10) = 4
  14.  
  15. φ(12) 12: 2*2*3
  16. φ(12) = 12*(1-1/2)*(1 – 1/3)
  17. φ(12) = 4
  18.  
  19. iii. Do you see a relationship between φ(p-1) and the number
  20. of gnerators modulo p for prime p?
  21.  
  22. Yes, there is a relationship. The number of generators modulo p for prime p are the numbers generated by Euler’s Totient.
Add Comment
Please, Sign In to add comment