Thread: phi function
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Old 2017-01-17, 09:56   #3
Nick
 
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Dec 2012
The Netherlands

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Here is a little more detail to axn's hint.

If n is prime then \(\phi(n)=n-1>n-\sqrt{n}\) since n>1.

If n is not prime then n=km for some integers k,m with 1<k<n and 1<m<n.
At least one of k and m is greater than or equal to \(\sqrt{n}\) and we may choose the names so that \(k\geq\sqrt{n}\).
Now \(\phi(n)\) equals the number of integers in the list 0,1,2,,...,n-1 which have no factor in common with n.
How many numbers in the list are multiples of m?
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