How many degree $\leq$ $d$ mod($p$) polynomials are there such that $P(a_1),...,P(a_k) \neq 0$ for $k < d$ and $0 < a_1 <...< a_k < p$, all integers? I considered subtracting out elements from the the set of all polynomials of degree less than or equal to $d$, but this didn't get me very far.
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A search shows that this is a homework problem 2c in Berkeley CS 70 – Calvin Lin Oct 08 '13 at 01:44
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The homework was already due. – Oct 08 '13 at 01:47
