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 whether a number is nontotient or not?
You first need to show that are all non-nontotient.
After that you need to show that is a non-totient number.
We want so that .
Write .
Then we have .
The RHS has only one factor of .
Therefore we cannot have where are odd primes.
The RHS has also a factor of .
This forces where and .
This never works to give .
Thus, is nontotient.