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Old 2019-04-17, 03:04   #9
dcheuk's Avatar
Jan 2019
Pittsburgh, PA

233 Posts

Originally Posted by MathDoggy View Post
Counterexample to Lehmer's totient problem
2^521-1 is prime and when you put in the Phi function it is not equal to (2^521-1)-1 as Lehmer conjectured
I am confounded. We all know that \(p\in\text{prime}\implies\phi(p)=p-1\), recall that the group of units for any prime number p has order (p-1).

How so that \(\phi\big(2^{521}-1\big)\neq(2^{521}-1)-1\) but \(2^{521}-1\) is a prime?
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