Solution
= Solution
{c}
Every integer has one of the six residues $0,1,2,3,4,5$ modulo $6$. A <prime number> other than $2$ or $3$ is divisible by neither $2$ nor $3$, eliminating residues $0,2,3,4$. Thus
$$
\boxed{p\equiv1\text{ or }-1\pmod6.}
$$