# Consecutive Quadratic Residues

For all prime numbers $$p$$ where $$p > 5$$, define $$C_p$$ to be the set of all positive integers $$k$$ such that $$k \le p-2$$ with $$k$$ and $$k+1$$ as quadratic residues modulo $$p$$. For example, $$C_{11} = \{3, 4\}$$, because $$3,4,5$$ are quadratic residues modulo 11 ($$5^2 \equiv 3, 2^2 \equiv 4, 4^2 \equiv 5 \pmod{11}$$).

It can be proven that $$C_p$$ is non-empty for all $$p$$. Let $$m_p$$ be the smallest element of $$C_p$$. Find the maximum value of $$m_p$$ among all $$p$$.

If this maximum doesn't exist, enter 0 as your answer.

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