Question 126
Find the smallest odd prime $p$ for which there exist positive co-prime integers $k$ and $\ell$, such that
$$
4k - 3\ell = 12 \quad \text{and} \quad \ell^2 + \ell k + k^2 \equiv 3 \pmod{p}.
$$
$$
4k - 3\ell = 12 \quad \text{and} \quad \ell^2 + \ell k + k^2 \equiv 3 \pmod{p}.
$$