A103314 conjecture

[Max]

Mitchell Harris wrote:
> On Fri, 20 May 2005, David Wilson wrote:
> 
> 
>>To: "David Wilson" <davidwwilson at comcast.net>
>>
>>> f(p) = 2 (obvious, either all or none) [f = A103314]
>>
>>Can you explain to me why it's obvious?
> 
> 
> It's not obvious that it is obvious.
> First it happens to be true for small primes (inspection and symmetry 
> confirms visually up to 7 for me). Trying to formalize it, the best I can 
> think up is a Vandermode matrix (from fast fourier transforms) which is 
> singular but removing any rows/columns is not (which of course is even 
> less obvious). Any simpler justifications?

I think the same follows from irreducibility of T_p(x)/x for odd prime p,
where T_p(x) is Chebyshev polynomial.
http://www.artofproblemsolving.com/Forum/topic-35047.html

Max