chiph588 1228079953|%e %b %Y, %H:%M %Z|agohover
A nontotient number 
is a number such that there is no 
where 
.
The smallest such number is 14.
My question is how would one prove for example that 14 is nontotient?
jensberg 1228108345|%e %b %Y, %H:%M %Z|agohover
I think that it's not that bad. But you also left out the fact that all odd numbers (excluding 1) are nontotient.
So remembering that 
is multiplicative, we note the following: suppose 
, with 
(there could be a 2 in there, but not more than one, since 
but that 4|
and 14 isn't divisible by 4). Then 
. But 2|
and 2|
and thus that implies that 4|
which would be impossible. And thus n cannot be a product of odd primes. So the only case left is that 
(again possibly times 2), and since p is odd let p = 2k+1, 
. But then 
which implies that 
. And then there's no k that makes that work (that would need to be more rigorous, but it's certainly a start).
