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Number Theory : Quadratic Residues

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Please provide a detailed solution to the attached problem. Please do not give a trivial answer. I think the questions asks us to determine the what form p is of (for example, p is a prime of the form 3n+1 (this was an example randomly chosen). I am trying to solve this problem myself (using that x^2-6 = 0 (mod p) => 6 is a quadratic residue mod p, and then try to find the form using the properties of the Legendre symbol (but if this is wrong, please discard it).

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Solution Summary

Quadratic residues are examined using number theory.

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