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?

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- November 30th 2008, 01:20 PMchiph588@Nontotient Number
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? - November 30th 2008, 01:50 PMThePerfectHacker
- November 30th 2008, 01:56 PMchiph588@
whoops, i forgot to mention the trivial answer of odd numbers...

- December 2nd 2008, 12:39 PMThePerfectHacker
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.