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- The generators for mod 13 are 2, 6, 7 and 11 because
- g^k is different for each k in 1...p-1
- ii. Compute φ(6), φ(10) and φ(12)
- φ(6) 6: 2*3
- φ(6) = 6*(1-1/2)*(1–1/3)
- φ(6) = 2
- φ(10) 10: 2*5
- φ(10) = 10 * (1 - ½) * (1 – 1/5)
- φ(10) = 4
- φ(12) 12: 2*2*3
- φ(12) = 12*(1-1/2)*(1 – 1/3)
- φ(12) = 4
- iii. Do you see a relationship between φ(p-1) and the number
- of gnerators modulo p for prime p?
- Yes, there is a relationship. The number of generators modulo p for prime p are the numbers generated by Euler’s Totient.
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