
#1
Apr2909, 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(21) * 5^99(51) = 2^199 * 5^99 * 4 = 2^201 * 5^99. I don't understand line 47. Can anyone explain? 



#2
Apr2909, 08:42 PM

Sci Advisor
HW Helper
P: 3,680

phi(p^a) = (p1)(p^(a1)) for p prime




#3
Apr3009, 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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