[seqfan] Re: A180634

[W. Edwin Clark]

I think it is true. Assume n > 2.

Use Gauss's generalization of Wilson's theorem
<http://en.wikipedia.org/wiki/Wilson%27s_theorem#Gauss.27s_generalization>,
namely, the product of the units of Z_n is -1 if n is 4 or p^i or 2p^i for
odd primes p, i >0,  and
is equal to 1 otherwise.

And assume that the comments and formula for A033949 are correct.


On Mon, Dec 8, 2014 at 7:11 PM, <israel at math.ubc.ca> wrote:

> A180634 is "Numbers n such that the discriminant of the n-th cyclotomic
> polynomial is a square". It appears to also coincide with n such that the
> product of elements in the group of invertible elements mod n (i.e. the
> product mod n of x such that 1 <= x < n and x is coprime to n) is 1. Is
> this true? An equivalent characterization of the latter (apart from n=2): n
> such that the number of square roots of 1 mod n is divisible by 4.
>
> Cheers,
> Robert
>
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