getting phi of a large number


by hanelliot
Tags: number
hanelliot
hanelliot is offline
#1
Apr29-09, 07:08 PM
P: 18
phi(20^100)
= phi(4^100 * 5^100)
= phi(2^200 * 5^100)
= (2^200 - 2^199)(5^100 - 5^99)
= 2^199(2-1) * 5^99(5-1)
= 2^199 * 5^99 * 4
= 2^201 * 5^99.

I don't understand line 4-7. Can anyone explain?
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CRGreathouse
CRGreathouse is offline
#2
Apr29-09, 08:42 PM
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P: 3,680
phi(p^a) = (p-1)(p^(a-1)) for p prime
matticus
matticus is offline
#3
Apr30-09, 02:50 PM
P: 107
also since phi is multiplicative phi(a*b) = phi(a)*phi(b) when gcd(a,b)=1


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