A103314 conjecture

[Mitchell Harris]

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?

Mitch