OpenStudy (asapbleh):

Find these values of the Euler function. Problem below.

3 years ago
OpenStudy (asapbleh):

\[\phi(10)\]

3 years ago
OpenStudy (jtvatsim):

The Euler function counts the number of positive integers less than a number that are relatively prime to it. So, the question is really asking: How many positive integers are there less than 10 and relatively prime to 10?

3 years ago
OpenStudy (asapbleh):

what is relatively prime?

3 years ago
OpenStudy (jtvatsim):

relatively prime numbers are numbers that have no factors in common. e.g. 16 and 49 are relatively prime since 16 = 2^4, 49 = 7^2 have no factors in common. however, 16 and 36 are not relatively prime since they share a factor of 2

3 years ago
OpenStudy (jtvatsim):

So for this question you need to decide which of: 1, 2, 3, 4, 5, 6, 7, 8, 9 are relatively prime to 10.

3 years ago
OpenStudy (jtvatsim):

what course are you taking to have encountered this question? :)

3 years ago
OpenStudy (asapbleh):

discrete mathematics

3 years ago
OpenStudy (asapbleh):

1,3,6,7,8,9

3 years ago
OpenStudy (asapbleh):

its probably wrong. sighhhhh

3 years ago
OpenStudy (jtvatsim):

6 and 8 both share a factor of 2 with 10. so the only ones that work are 1, 3, 7, 9

3 years ago
OpenStudy (jtvatsim):

A good practice is to factor each number into primes and compare the factors directly. :)

3 years ago
OpenStudy (jtvatsim):

if a number share even a single factor in common with 10, then there is no way they can be relatively prime.

3 years ago
OpenStudy (jtvatsim):

In any case, the answer is \[\phi(10) = 4\] since there are exactly 4 numbers less than and relatively prime to 10.

3 years ago
OpenStudy (asapbleh):

Ohhhhhh Isee now. Omg i get it. Thanks

3 years ago