



Cant remember having that in the exam o.o. Or was it?R4man18 said:If N = pq with p and q primes
then phi(N) = (p - 1)(q - 1)
phi(N) = (p - 1)(q - 1) = pq + 1 - (p + q)
A = N + 1 - [3/sqrt(2)] sqrt(N)
A = pq + 1 - [3/sqrt(2)] sqrt(pq)
phi(N) > A p + q < [3/sqrt(2)] sqrt(pq)
2p² + 4pq + 2q² < 9pq
2p² - 5pq + 2q² < 0
(2p - q)(p - 2q) < 0
it's true because p > q thus 2p - q > 0
and p < 2q thus p - 2q < 0
B = N - 2sqrt(N) = pq - 2sqrt(pq)
phi(N) < B 1 - (p + q) < - 2sqrt(pq)
p + q - 2sqrt(pq) > 1
[sqrt(p) - sqrt(q)]² > 1
sqrt(p) - sqrt(q) > 1 (because p > q)
N >= 6 (for p = 3 and q = 2)
then p - q > 6^(1/4) > 1.5
p > q + 1.5
sqrt(p) > sqrt(q + 1.5) > sqrt(q) + sqrt(1.5) > sqrt(q) + 1
thus sqrt(p) - sqrt(q) > 1 and phi(N) < B
and
A < phi(N) < B
taken from yahoo

Just make it up manCalafas said:If it asks me for any old memories or whatever, i'm gonna hafta b/s it, seeing as how i have a shit memory.![]()
And I hate writing about that stuff.![]()
But oh well, no exams tomorra![]()
Just hafta revise for English on Thrusday. :/
Dont worry, the media will be easy.leonheart_a said:Man that english exam was a bitch ¬.¬.
I officlally hate poetry even more. Your lucky your english was easy![]()
I think my media paper should be good though![]()