Let p be a prime =1 (mod 5). Necessary and sufficient conditions are determined for the prime q (q 19) to be a quintic residue of p.The results for q 7 are known, the rest are new.

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Persistent URL dx.doi.org/10.1090/S0025-5718-1976-0412089-9
Journal Mathematics of Computation
Williams, K.S. (1976). Explicit criteria for quintic residuacity. Mathematics of Computation, 30(136), 847–853. doi:10.1090/S0025-5718-1976-0412089-9