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Oxymoron
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And with per(1/p^2) we can say that it too is a divisor of phi(p^2). Which, as you have already said, means that per(1/p^2) divides p*(p-1)
Posted by Shmoe
Yes, but you can also say something about per(1/pq) in terms of per(1/p) and per(1/q), namely per(1/pq) = lcm(per(1/p),per(1/q))
Oxymoron said:I thought we came to the conclusion that this wasnt true. It was because per(1/7) happened to equal phi(7), and per(1/17) happened to equal phi(17). Now you are saying that it was correct.
Oxymoron said:5. We know that t divides ord_p(10) <=> 10^t=1(mod p)
6. We know that t divides ord_q(10) <=> 10^t=1(mod q)
Oxymoron said:7. We also know that ord_p(10) divides p-1 (or in other words phi(p)).
Oxymoron said:8. From 4a and 4b we know that if t divides two different numbers then it must divide their lowest common multiple. That is, t must divide lcm(ord_p(10),ord_q(10)).
Oxymoron said:9. Which means that t divides lcm(phi(p),phi(q)).