- #1

- 18

- 0

= 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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- Thread starter hanelliot
- Start date

- #1

- 18

- 0

= 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?

- #2

CRGreathouse

Science Advisor

Homework Helper

- 2,824

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phi(p^a) = (p-1)(p^(a-1)) for p prime

- #3

- 107

- 1

also since phi is multiplicative phi(a*b) = phi(a)*phi(b) when gcd(a,b)=1

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