The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p)=
a. p-1
b. p-2
c. (p+1)/2
d. (p-1)/2
e. 2
OA: A
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For a prime number p, all positive integers less than p has no positive factor in common with p other than 1. Hence number of such positive integers, i.e. f(p) = Number of positive integers less than p = (p - 1)trangle wrote:The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p)=
a. p-1
b. p-2
c. (p+1)/2
d. (p-1)/2
e. 2
The correct answer is A.
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Plug in a value for p.trangle wrote:The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p)=
a. p-1
b. p-2
c. (p+1)/2
d. (p-1)/2
e. 2
OA: A
Let p = 5.
f(5) = the number of positive integers less than 5 that have no factor in common with 5 other than 1.
Since 1, 2, 3, and 4 = 4 integers that have no factor in common with 5, f(5) = 4. This is our target.
Now plug p = 5 into all the answer choices to see which yields our target of 4.
Only answer choice A works:
p-1 = 5-1 = 4.
The correct answer is A.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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