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Why is Euler's totient function never equal to n/4?

For Euler's phi function why does phi(n) never equal n/4 for a positive integer n? I'm doing a past exam paper and this is one of the questions, but there are no solutions provided so I don't know if my proof is solid.

Reply 1

BabyMaths

Phi(n)=n(p-1)/p........

Phi(n)=n/4 implies 1/4= a fraction where the denominator is a product of primes.

Reply 2

ooerr

Original post by BabyMaths

Phi(n)=n(p-1)/p........

Phi(n)=n/4 implies 1/4= a fraction where the denominator is a product of primes.

Do you mean because 4 cannot be equal to a product of distinct primes?

Reply 3

S.R

What is the point in the totient function?

Reply 4

ooerr

Original post by S.R

What is the point in the totient function?

phi(n) = the number of integers between 1 and n that are coprime to n

Reply 5

S.R

Original post by ooerr

phi(n) = the number of integers between 1 and n that are coprime to n

I see. And wikipedia says that the probability that two numbers are coprime = 6/pi^2 because the totient function becomes an infinite product that is the same as the zeta function. Mindblowing stuff.