2. (a) In lecture, we saw Euler’s Totient Function Φ(n), which is defined as the number...
2. (a) In lecture, we saw Euler’s Totient Function Φ(n), which is defined as the number of positive integers less than or equal to n that are relatively prime to n. Suppose I want to compute Φ(84), as per lecture. I know that 84 = 14 × 6, so I compute Φ(14) and multiply it by Φ(6). Do I get the right result? Briefly, why does this work or not work? Your answer should be brief, but not as simple as “because the numbers do/don’t multiply to form that.” (b) Compute Φ(84). Show your work.
Homework Answers
(84) = 24
(6) = 2 {1,5}
(14) =
6 {1,3,5,9,11,13}
Reason -> Euler's totient function is a multiplicative
function.It means if there are two numbers a and b are relatively
prime then
(m*n) = (m)*(n).
And in above case
gcd(6,14) = 2 //greatest common divisor
it means 6 and 14 are not relatively prime.So here,
(84) is not
equal to (14)*(6)
24 != 2*6
24 != 12
for more understanding lets take 84 = 21*4 {21,4 are relatively
prime gcd(4,21) == 1}
(4) = 2{1,3}
(21) =12
(84) = (4)*(21)
24 = 2*12
24 = 24
If you have any doubt.Please feel free to ask.Thanks
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what code in R should I use if I want to achieve 10 different
outputs with the same n. n= a number that doesnt satisfies the CLT
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with 10 different values of n.
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