Question 46
Determine whether or not there exists a positive integer $k$ such that $p = 6k + 1$ is prime and
$$
\binom{3k}{k} \equiv 1 \pmod{p}.
$$
(This problem was suggested by Gabriel Carroll.)
$$
\binom{3k}{k} \equiv 1 \pmod{p}.
$$
(This problem was suggested by Gabriel Carroll.)