Solution
= Solution
{c}
Over the <finite field> $F=\mathbb Z_p$, a <basis> of the <hyperplane> has $n-1$ <vectors> by <2/a/ii>. Each <vector> on the <hyperplane> has a unique expression as a <linear combination> of that <basis>, and each <coefficient> has $p$ possibilities. Thus
$$
\boxed{|H|=p^{\,n-1}.}
$$
Equivalently, choose freely all coordinates except $x_j$, where $a_j\ne0$, and solve uniquely for $x_j$. For $n=1$ this counts just the <zero vector>, consistently with $p^0=1$.