if (n-1) is divisible by φ(n) then there is no prime p such that p^2|m.

Thanks...

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- Nov 29th 2011, 05:42 AMseventhsoneuler fhi function and power of a prime
if (n-1) is divisible by φ(n) then there is no prime p such that p^2|m.

Thanks... - Nov 29th 2011, 11:54 AMPaulRSRe: euler fhi function and power of a prime
I suppose you meant to say .

Let's proceed by contradiction, suppose on the contrary that there were a prime such that . Clearly since and are coprime, however implies , and since we have that which is a contradiction.

Check this by using the formula , where the products runs over all primes dividing . - Dec 1st 2011, 01:09 PMseventhsonRe: euler fhi function and power of a prime
Thank you Paul for your nice proof...